Yes they would. And they'd have to make canon several things:
1> outcome of the quarian and geth
2> outcome of the rachni
3> outcome of the genophage
4> the ending - was it synthesis?
Like it or not it is best to avoid the outcomes completely. It avoids the amount of rage. The Ark leaves right after the fall of Thessia.
No, there are workarounds for everything you listed.
1) There were some survivors on both sides. Some Quarians could have left the flotilla when the decision to attack the Geth was made. Some Geth could have been outside the system Rannoch is in so avoided the battle. We know there are survivors on both sides already. As for the Geth being killed in Destroy, they were rebuilt.
2) The Rachni laid a Queen Egg that was taken. We know the Salarians tend to do this kind of thing.
3) Krogans will be around for tens of thousands of years whether or not the Genophage was cured.
4) The endings can easily be worked into a state where they are gameplay-wise functionally the same.
The things I listed would require some alternate dialogue and the use of the Codex, but like I said Bioware has done that for years now.
No, it is not the best. It is the easiest. There is a difference.