The trademark of S.T.E.A.M. is for a Japan market game. Most likely for 3DS if anything at all. It is a really poor name especially what it stands for.
Anyway, your idea of a Nintendo FPS game is to copy elements of bunch of other shooter games? Nintendo just doesn't roll like that. If they didn't think it up, then they wont do it even if they recognize that it is a good game design / gameplay whatever.
The reason is very simple, you can already play those other games. Nintendo is much more interested in new gaming experiences or keeping their existing franchises alive and relevant.







