The thing about having a character created to deal with particular types of foes and terrain is that it's a signal to the DM to make those things important in the campaign. Unfortunately, similar abilities are pretty rare in 5e, and the DMG is far more interested in telling people how to invent a cosmology from scratch, rather than sitting them down and saying 'look at your player's character sheets and work from there.' Published adventures are of course not much help, either.
So, while I think abilities like Favoured Foe are cool and flavourful, I don't think they fit the game as it exists, or at least, as many people play it.