Sacrosanct
Legend
The problem I have with feats is that too often players choose feats that make them even better at what they do (usually combat), rather than adding extra abilities (especially non-combat). We have two GM's. I don't allow feats, but the other GM does. The type of feat selection I mentioned above has been the pattern in his games. Even checking the boards here, I've lost count of the number of posts where it's assumed a character took Great Weapon Master, Polearm Master, Sharpshooter, and Crossbow Expert. Except for fighters, most characters don't get a lot of feats, so it's natural for players to choose feats with the most "oomph", but that (to me) just makes things more "samey".
What I'd like to see (and may come up with for my own table) are feats that are less combat-focused and more concept-focused. If I do it right, they should still be useful, but more in the way of expanding a character's options as opposed to just reinforcing what the character already does. I'd especially like to see feats that allow one to partially take on another class's role without requiring multiclassing, such as my Outdoorsman feat above.
A lot of people tend to gravitate to the optimization choices. I think in order to do what you want, you'd have to put a limitation to something like, "With the extra feats at level 6 and whatever, you can use an ASI or any feat except these ones..." or "only from this list". I know some players might not like that. I guess it depends on what you want vs what the players want. Many players (like myself and it sounds like you), have no problems with choosing non combat feats to flesh out a role or theme that we want. I have a fighter right now who has dungeon delver and skulker feats (he was ported over from my halfling f/t in AD&D to just straight fighter in 5e).