Why are there no Reapers in Andromeda?

Of course there are similarities between the enthrallment and indoctrination. We are told that the Reapers perfected that technique. There are differences though, like indoctrination never causes the 'cold and dark' sensations that Leviathan does. 
We see three Leviathans. 

Even if Leviathan is a rebel Reaper, why would he lie about their origins? He has no logical reason to, and the Reapers are all about logic. 

Thank you.
My point has been concluded.

If your tin-foil theory that the Leviathan was merely a rogue Reaper was true, what would the point be in Leviathan going from the nigh-invulnerable Reaper shell to an organic, squishier form, without access to in-built weapons?

That'd be such an massive (and totally idiotic) downgrade, it'd be like if Shepard ripped out all their cybernetic implants and their reinforced skeletal structure, replaced them with Joker's brittle bones, then decided to pick a fight with a Krogan.

Otherwise, are we supposed to believe that it actually looks like a Reaper, but created a complicated vision of itself as a squid and a crazy mindscape for Shepard, all for the purposes of telling it a completely fabricated story that would serve no purpose?

If you remember, until Shepard convinced them to enter the conflict to get their revenge, the Leviathan were planning to remain hidden as they always had done. They had no reason to manipulate Shepard by giving them a false history of the Reapers's origins, since they were never planning to let Shepard leave their underwater lair in the first place.

Since the most simplest explanation is usually the correct one... then the simplest answer is the one given, the Leviathans are the big dumb jellyfish squids who accidentally unleashed the Reapers, after their AI admin went amok because they gave it bad instructions.

The end goal of the Andromeda Initiative is to build more Mass Relays in Andromeda, as well as try to find a way to link back to the Milky Way network (assuming it still exists). So we will eventually be getting Mass Relays, the colonists simply have to build them first.

Andromeda is 3 times the size of the Milky Way and is two times older.

No it isn't. The Milky Way is around 13 billion years old and Andromeda is around 9 billion years old. 

That's why I hate ME3. Because reapers in this part are just stupid machines. And their goal is completely dumb. During first two parts of ME reapers were introduced like thinking beings, a mix of synthetic and organic life. Remember conversation with Sovereign? Did he look like stupid machine?

Yep.
There's no reason to think Andromeda isn't civilised enough or never has been because they also have their mysterious ancient race , I believe.The Not! Prothean ?
I haven't followed everything about MEA.

Honestly my brain wants to flush everything about the Reapers away, so I don't really want to think about synthetic/organics in Andromeda.
But again it's a damn if you do , damn if you don't.
Speaking for myself I'd rather the writers/devs just ignore the issue altogether "Oh no something awful happened and we're forever cut off from the Milky Ways...!!!!".
There's also the question that even if Andromeda for unknown reason doesn't have powerful AI/VI yet , well we're bringing some and we're bringing the knowledge over.It's the equivalent of bringing the apocalypse if you believe the Reapers.
So it might be better if this is ignored , and there's no reasons for the npcs in MEA to be aware of that anyway , since they are living before things went really south and the catalyst speech.

Why would any sane Andromedian create anything like the Reapers?

Andromeda hasn't had a billion years of cycles of destruction/.  Forget the protheans, there should be something like the Leviathans at the height of their power!

Indoctrination appears to be a permanent state.  Enthrallment can be permanent but can also go away with no aftereffects.  Both can be a slow process.  However, the mere presence of a Reaper or Reaper tech causes indoctrination whereas simply being around a Leviathan or its tech may doesn't cause enthrallment (thought does appear to make a person more susceptible to it if the Leviathan chooses).

Re: Atemporal Vanguardian-Debugger: No, I can't see the Leviathan as a rebel Reaper.  It's an entirely organic entity versus organic goop loaded into a machine.  Reapers are, for lack of a better description, synthetic versions of Leviathans.  The first Reaper was Harbinger who was from the first harvested race - the Leviathans.  It was created by the Intelligence/Catalyst in the image of its own creators, the Leviathans.  The Leviathan Shepard meets even acknowledges that they couldn't imagine that an AI could pose a threat them, even though they believed AI were a threat to all of the "lesser" races.

Maybe, but we haven't seen anything like them in real life.  Why assume it has to be the case?  A species could die or stagnant for any number of reasons that would prevent us from seeing an all-powerful race that controls the entire galaxy.  Practically speaking, had the Leviathan not created the Intelligence, perhaps they would have died off.  Alternately, they might have expanded into other galaxies (though given that we have about 100 billion stars in the MW, and we've seen nothing to suggest that the Council races are connected to all of them, it seems unlikely).