1. Staying in the Milky Way restricts creativity since they have to not only account for the fallout of the endings, but also deal with other issues in a galaxy that could be so vastly changed by those final choices that it may as well be a Galaxy Far Far Away.
2. Moving out of the Milky Way forces the audiences to deal with place that is no longer familiar, to reconsider what they thought they knew, and have no quick and easy route back to familiar space. You are alone, with no calvery coming through the gate to save you if you screw this up.
3. A chance to see how the old races on the whole deal with a new challenges, and introduce technology vastly different from that of the Reapers while still keeping that Reaper tech aesthetic for the MW Races.
4. Having an entire galaxy to expand to in future games provides more options than unopened relays scattered across the Milky Way. It also forces the races to build new colonies without the oversight of the council (for good or ill)
There is a way to stay in the same galaxy without having to deal with the choices of the trilogy
It gives a whole new playground without any influence from the Council (and all the other governments)
To clarify, I don't suggest exploring the places we have already seen. This sector of space will be entirely separate from the locations of the trilogy.
Points 2,3,4 still apply here.
The only thing that needs to be addressed is how the wave doesn't reach there. But then again, they need to address intergalactic travel for Andromeda, as well as travel within the new galaxy.
And I don't think that the game set in Andromeda or any other galaxy will necessarily be bad. I just think that going there now is not the best option available to them.