Ratskinner
Adventurer
Yes, and as I mentioned in my previous post, I'd even remove prerequisites so that you won't have to filter out any feat because they would all apply.
Prerequisites makes sense (a) for feats that obviously improve a specific ability, so that if you don't have it at all then the feat doesn't apply [ex. a metamagic feat requires you to be a spellcaster], (b) when the feat has a variable effect depending on a bonus but you might have a penalty [ex. a feat granting your Wis bonus to AC requires you to have minimum +1 Wis], (c) in feat chains.
(a) and (b) are actually implicit prerequisites, and if we want to make all feats for everyone then case (a) goes away. Requisites for (c) should really be there only when a feat is a direct improvement of a previous feat, but they are not needed at all if the 2 feats in a chain follow a general theme but are effectively separate abilities, such as
Power Attack - Cleave (and many others) in 3ed. Why can't a PC learn Cleave without PA, since she's not using PA while using Cleave? This just becomes a "feat tax" and restricts character design flexibility.
I think the point is...that you don't really have an awful lot of design space or function left remaining for the feats. At least, not and make them worth getting one so often as we are used to. I mean, if I were re-doing 3e, I'd definitely re-examine feat design and structure using thoughts very similar to yours (both from this post and previous.) However, with maneuvers for fighters and expertise-y stuff for rogues...5e simply doesn't need them as much. The primary purpose behind feats is to make Fighter A different from Fighter B. If you have maneuvers that's gone because you have a better way to do it.
I do not agree that feats are such a stunning mechanic that "...it really would be a pity to remove it as a whole from the game, it's the ultimate game mechanic for character customization..." While I think that a few relatively universal "themes" or the like could hang around, things like the Stark kids' wolves as familiars are better handled as a DM just giving them the familiars. Which, I think, would make a fine example for the DMG "making the game your own" chapter.