Beyond the flawed logic of the Catalyst, why was this never explained?

There's that straw man again.  He probably should have.  I think he just forgot.

Because Catalyst was the Prothean term for it much like Reaper was Prothean term for it.  At least with Reaper there is a connection to be made so they know about it.

What does Shepard not asking Leviathan have to do with the point that they can call the same thing both intelligent and a catalyst.

You're the one with the agenda here to prove up "bad writing theory."  I just entered the conversation here saying that the terms used are not mutually exclusive of each.  The Catalyst can be both a catalyst and an intelligence.  Your asking why they called it two different things is the straw man here since it has nothing to do with whether or not Shepard asked about it.

Bioware's selection of naming terms for both has to do with forms of change.  I don't think that's accidental.  It's more likely symbolic, just as a number of the other names they use for things are symbolic and suggestive of different themes in the game.  Even Shepard's name being suggestive of Jesus is symbolic and does tie into where the game takes his character in the end.

Catalyst - "a person or thing that precipitates an event." and "a substance that increases the rate of a chemical reaction without itself undergoing any permanent chemical change."

Crucible - "a place or situation in which concentrated forces interact to cause or influence change or development"

Furthermore, what differentiates an AI from a VI in the mass effect universe is being "self-aware" and, in relation to EDI, the idea of being able to make changes to oneself (discussed on the bridge and discussed with Javik in the AI Core).

Synthesis is a change.  So is replacement of one Catalyst with another (control), and so is the total destruction of the Reapers since the status quo for the last several millenia has been that reaper harvest all sapient species in the galalxy every 50,000 years.

There is also an element of Control in the definition of the term "citadel":  "a fortress that commands a city and is used in the control of the inhabitants and in defense during attack or siege." www.dictionary.com/browse/citadel

Because it would have resulted in not getting a answer thus making the whole action ultimately a waste of time to bother to do. 

Without asking the question, there is no way to know if there would have been an answer. Right? How much time would have been wasted? A few seconds?

 A few seconds that is a waste of resources.   Leviathan know the Intelligence is out there. It knows about the Reaper cycle having hidden from it on a blacked out planet. There would be no way for them to know the Intelligence is on the Citadel.   Asking would result in no answer and would be a waste of resources to do so. So why bother with it?

I mean if you ever develop a game feel free to add all the redundant and meaningless voice acting and animation to it you want.  But I wouldn't bother with it because it's answer is fairly obvious to anyone paying attention. I'm not going to waste money to hand hold the minuscule amount of players that couldn't put two and two together on their own.

Not to mention that "The Leviathan of Dis" was an offshoot note Chris L'Etoile or Hepler wrote into a planetary codex in ME1 or ME2 without any further lore. Then BioWare used it as an opportunity for DLC because there was no context for the Catalyst. Period.

.... and I've said they had the same sort of lack of foreshadowing about Seeker Swarms carrying off people in ME2 and about the Conduit being a back door onto the Citadel plaza in ME1.  Of the three endgames, the idea of the catalyst being a means for Shepard to change the course of the war and alter the cyclic pattern established in the galaxy was far more predictable than the other two.  That it could also be an artificial intelligence seems also predictable to me... and I did not have the Leviathan DLC the time first I played through ME3.  Without the Leviathan DLC, the codex entries from ME1 would have simply been fluff techno-babble entries that led no where... like so many others of those planetary entries from ME1 and ME2.  Put there for the people who like to stock up on meaningless trivia.

You don't want to see a context... just as you don't want to admit there was no context for the change in behavior of seeker swarms nor any context for the Conduit leading us right back to the Citadel... because that would show that the plot planning and foreshadowing in ME1 was every bit as "bad" as in ME3.

... and the Catalyst is being built up as the "missing component" of the Crucible throughout the entire game.  The characters in ME3 keep talking about not really knowing what the Crucible does.  Without knowing what the Crucible does... it's really hard for them to even start to wonder what the Catalyst for making it do whatever it does would be like... but you always know through the entire game that it is the "trigger mechanism" for firing that Crucible... and ultimately, that's was Starbrat is... because, enemy or no, he's the one who ultimately explains how the whole device works.

The idea is telegraphed in almost exactly the same way as the Conduit is... and then they (Bioware) pull their switcheroo with both and neither actually does what you thought it might.  It's the same damn thing in both games.

My expectation for the Conduit was that it was a Mass Relay gateway directly to the Reaper base... not a one-way, mini-me version of a mass relay that would just take me back to a public plaza on the Citadel (the place I had just left from to go chasing off all the way to Ilos).  That part was never telegraphed anywhere in the game prior to meeting Vigil on Ilos.

Yes. The Catalyst is a term referring to the missing, unknown component that makes the Crucible work. That turns out to be the citadel. It's like having a variable X that then turns out to be number 1, they're one and the same but one is an alias.

That's why I'm not completely torn about the Existence of the AI on the Citadel. It makes sense to me. I think of the child as being a representation of the AI that is the Citadel and I think of the Citadel as a giant but faceless Reaper-structure (that also doesn't indoctrinate) or like the Normandy where the metal surfaces of the Citadel is like the skin the same way EDI says she can feel herself through the normandy after getting unshackled in ME2.

The Crucible needs the Citadel to work, which is the Catalyst and the child is just a pop-up message that makes you able to interact with the Citadel's AI as hologram. The citadel contains the actual function of the Crucible when the energy is released and the Crucible is just the thing generating the energy. The big million dollar question is how did Vendetta VI, a prothean construct, know about the Citadel having an AI that uses the Crucible to fire it if the Starchild reveals that Shepard is the first organic to know of its existence? It probably comes down to the fact that protheans have their info about the Crucible passed down from several cycles and the Crucible originates from the cycle that started it all when it was being developed alongside the Catalyst's solution.

You could think of it as the Crucible being the organic species of Leviathan's time making an attempt to create a solution for the issues about organics and synthetics while the Catalyst found a "synthetic" solution but in the end the organic solution (the crucible) needed the synthetic solution (the Catalyst/Citadel/Reapers) to make the ultimate solution.

Its possible.

It could be the keepers that made the plans. They know the Citadel inside and out. Do they know about the catalyst? Don't know. I'm sure the plans they made were for a device that was designed to destroy the reapers. Over countless cycles, each adding something without knowing what they added would do anything. Its possible one of the species wanted to control the reapers to control them. So they added stuff that might be able to do that. The next cycle adds whatever without ever knowing one of the choices is to control the reapers. Many cycles later, another species decide they want to be buddy-buddy with the machines so they came up with the green choice without ever knowing if that would work. The next cycles adds whatever without knowing about the additions that can do whatever. Along comes our cycle. Its believe the device can destroy the reapers, but  don't know about the other possible choices. Shepard meets the thing. The player learns about the colors.

I don't know. I'm likely wrong about that.

I don't see the two ideas as being mutually exclusive either.  Sovereign indicates the idea that the Reapers are directing the paths along which OUR technology develops by having given us the Mass Relays... So this could include having "seeded" the idea for the Crucible.  If it's ultimate goal is synthesis, then it has a vested interest in ultimately seeing a Crucible build that can effect the outcome.  However, the contradiction to this sort of scenario lies in the Catalyst's admission that "we" (i.e. he and the Reapers) thought that the concept had been eradicated"... perhaps indicating that the technology had taken a "path" that was unforeseen and, hence, undesired, by the Catalyst and Reapers.

I don't think we're meant to really know for sure just how much of what Shepard has been doing is just following the same doomed path as other cycles and how much of it is taking this cycle into previously "undiscovered" territory.

ETA:  One thing that intrigues me is that the galaxy map that appears when Vendetta is describing how each cycle repeats itself is the same pattern as the wave of energy that comes from the Crucible being fired by Shepard... and it's red (just like in the destroy ending).  Is destroy breaking the cycle... or just repeating it?  Maybe what we destroy are just "clone Reapers" with the knowledge of all the past species they encompass still being stored in some "safe" archive out in dark space somewhere.  Maybe they don't actually retreat to dark space and hibernate... maybe they have actually been destroyed at the end of every previous cycle and it just takes 50,000 years to rebuild the Reaper fleet to start another harvest all over again?  Maybe, as Barla Von indicated right at the start in ME1... this is a game we just can't win.