Should bioware do one final shepard game?

Well, the first type of endings you listed are essentially the ME1 style where the sole hero magically solves everything with no consequence and no sacrifice involved... nothing dependent on whether or not the hero was a "paragon" or a "renegade."  If not based on a one-liner of red or blue dialogue, what did you expect your hero to be able to do to "save everyone."  Lob a grenade at Harbinger and have him just die because the grenade hit his "Achilles heel?"... followed by all his minions leaving the galaxy and swearing never to return because "OMG, the boss is dead?"

ME3 set up the notion that you were spending the game building some sort of doomsday weapon and you didn't even know what it does.  At the very end, you find out that it does NOTHING really good... the galaxy has blown the chance at a happy ending for all.  Now, you have no time to poll the galaxy, to see what outcome they prefer.  You have to choose and the choices are nothing really good... but it is a choice you can make based on what your Shepard believed throughout the games.  Ideologically, who did he side with the most - Anderson or TIM or neither.

I would argue that, if Shepard is the sort of hero who is mostly concerned with upholding free will, then the fact that the destroy ending results in the destruction fo the geth shouldn't be a concern... in that such a person would not have allowed Legion to violate the free will of the geth by uplifting them without their permission by uploading Reaper code.  In that case, the Quarians would have destroyed them before the ending and the only individual who dies as a result of destroy (other than possibly Shepard) is EDI.  Collateral damage of 1 individual in a galactic war is certainly not excessive.

NOTE:  I'm in no way agreeing that this should be made the canon ending though.

She's a computer program that is located in the server room on the Normandy. She wasn't there when the original Normandy was smashed.

Uh huh. How does your crew know Anderson died? No one told them. Only person who knows is Shepard, because he saw him die. I have my doubts on that scene.

And how does the guy know the details about what happened on the Citadel if all are dead? Only one survives, Shepard. Shepard tells the first story that is passed down to others who tell the story and so on and so on.

Good question about Anderson one that I've asked many times. How would they know Anderson and even Shepard are dead? How much time has past from when the crucible fired to the memorial scene? One scenario I posted is that someone from C-Sec, possibly Bailey finds Shepard's body while another finds Anderson's body. He call's Hackett to inform him that Anderson is dead and that Shepard is dead/alive. Hackett then forwards the message to the Normandy. Of course that scenario is only for the red. What about the blue and green? If anything, Shepard should be MIA.

As far as the edibot being destroyed by Harbinger. Here's it being destroyed

And here is the memorial scene without its name on the wall and the platform not in the scene.

However, in two of the ending scenarios, there is no body of Shepard's to find.  Technically, he/she would be MIA (presumed dead).  The point at which a service takes place, if at all, depends then on the point the family gives up hope of finding the victim alive.  Anderson's body could be found by Bailey (or other people who managed to stay alive without leaving the Citadel) or found by a crew sent up from earth to investigate the status of the Citadel.  Upon finding Anderson and not finding anything of Shepard, they would make the MIA (presumed dead) call based on Hackett's knowledge (through comms) that Anderson and Shepard were together near that console near the end.

Similarly, not placing the plaque on the Memorial Wall really doesn't say that the LI knows for certain that Shepard is alive or dead.  It really just says they are holding onto hope that he/she is still alive.

The amount of time elapsed before the Memorial Wall scene is unclear.  It's only the mods (like the Happy Ending one) that try to say it happens soon after since Shepard is shown still showing the signs of the injuries he/she sustained during the final battle.  It seems clear that it takes place before the Normandy flies off the planet it crashed on... but it could have taken a long time to repair the Normandy so it could fly again.

The presumption of death in absentia is the legal term for it.  Concise explantion per Wikipedia:  "A person may be legally declared dead in absentia, i.e. a legal presumption of death may be declared, despite the absence of direct proof of the person's death, such as the finding of remains (e.g., a corpse or skeleton) attributable to that person. Such a declaration is typically made when a person has been missing for an extended period of time and in the absence of any evidence that the person is still alive – or after a much shorter period but where the circumstances surrounding a person's disappearance overwhelmingly support the belief that the person has died (e.g., an airplane crash)."  This is likely what the Alliance did when Shepard went missing in ME2.  The LI putting the plaque on the Memorial Wall is not proof of life or death... just an indication of what they hope at that point.

As for Anderson, the crew may have a clear idea that Anderson is dead because he died before that final comms conversation between Hackett and Shepard.  From Shepard's obvious weakness during that last comms, it is possible for them to also hold the belief that Shepard was doomed to die at that point... meaning the circumstances were sufficient to declare him/her "dead in abasentia."

The damage you see to the ship may be irrelevant... depending on how you answer the question regarding how thoroughly EDI's processes are now dispersed throughout the ship... keeping in mind she has also been altering her core programming throughout ME3.  Even with minimal visual damage, the ship might take some time to be able to fly again.  It's a variable deliberately left vague so as to suit whatever the player wants to believe (dependent on the choices they make).