Apologies I meant Andromeda not ME3 :)
There is a core team introducing new features, taking features from other games an integrating, and as far as I remember (this was a few years ago) a library of features you could plug into the engine made by other development teams.
And yeah, the more different your game is from what Frosted already does (at the time, it was mainly FPS engine) a team would have to do significant work on the tech and game side of things... which is why the first few years of all these other genres on Frostbite aren't the best. BUT, if you look at the long term plan of 10 years, the games should get better and better as more teams and genres put work into it. There is no reason FrostEd couldn't do every game, it's just a budget/time concern, especially in the early days of the engine when it only did one thing very well (FPS).
And yes, I totally agree with you about the scalability of assets, which is why EA has been pushing development teams to work similarly as well. Dice start doing a really great job with photogrammetry and that is being touted around EA as a preferred method of creation. Again, so everyone can share assets. They did that for the first Battlefront where they got access to the Lucas Vault and photo "scanned" all the old props. I have zero doubt they will be leveraging this for every Star Wars game they make, but this is purely a guess on my part.
Concerning the conversation with Inquisition and Andromeda, I have some personal opinions.
Fitting Inquisition game type into Frost Ed is not a bad idea, but it comes down to money and time, there is only so much a team can do on the first iteration.. So did it hurt Inquisition? Yes, but did it hurt the franchise? Probably not, they have something to build on and it will get better. My own opinion is that design and direction choices were a larger contribution to why some (myself included) didn't quite like Inquisition.
Concerning Andromeda, similarly answer with Inquisition, though I Andromeda severely less successful (in terms of of a good game). Part of that again, is likely due to FrostEd, though they had Inquisition to build from, sort of, which should have put them in a better spot. They also had something like 6 years of development time, so what made Andromeda, Andromeda, again relies on direction choices more than tech.
I don't know anything about the development of Andromeda, but as a fan of the original trilogy and someone with partial knowledge of an older Frostbite engine, I could guarantee you that a good Mass Effect game can be made in that with the right choices for a lot less time than 6 years. Sorry to armchair quarterback,;I am more than aware of the difficulties any developer can go through, but it had to boil down to poor direction and decision making on that project.