They move on because the ending is over with. it's done. It's in the past. The writers don't have to spend the next decade whimpering over if the story they want to tell makes sense alongside the super-duper advanced Synthesis humanity or whatever. They don't have to be chained to it anymore.
Either this '****,' as you say, is dealt with and buried now, or it stays to rot and fester for the next few games. It's not going away.
I don't think that's really accurate - the entire point of going to Andromeda is that they're going to forget about the endings and probably never return to them. This will be the setting of the Mass Effect games, period, for the foreseeable future.
By the looks of it, Bioware are totally capable of writing a new story in Andromeda that has nothing to do with Shepard or the ending choices, and if it's successful then we'll just carry on with new stories in a new galaxy. There's absolutely no requirement to address the endings. How will it "fester and rot" if everyone is talking about new characters, new races and the new plot of this game?
I also don't see how it'll matter in ten years, regardless. What game series is around for fifteen to twenty years in total? We'll be supremely lucky if there's another trilogy of games, and if Mass Effect is still profitable then they can just keep setting stuff in Andromeda - assuming the writers don't write themselves into a corner again.
tl;dr: Shepard's story is over and I don't think the writers will revisit the consequences of ME3's ending choices. It's all new stuff from here on out.