It seems to me you're contradicting yourself. You say they are the "biggest failure", and then list the reasons why they aren't so bad and thus you allow them. Since this thread is dedicated to discussing feats, I think it's safe to say that no one would be bored to hear your reasons. I am curious to know your reasons for thinking of them as the "biggest failure", despite your good reasons for allowing them.
Well, in my defense 1) feats are the biggest failure in the context of 5e which I consider a tremendously successful game design, 2) as a DM they bother me less because I can ignore them; as a player they drive me nuts, and 3) as a DM I retain the right to contradict myself whenever I please.
Reasons I hate the 5e feat system:
1. Concept redundancy. By which I mean, I prefer to come up with a character concept first and then select the build options supporting that concept. Many feats muddy the waters considerably by being redundant, conceptually, with abilities, skills, and class features.
For example, which character is more "athletic?"
- The one with high Strength.
- The one with mediocre Strength and proficiency in Athletics.
- The one with low Strength and Expertise in Athletics.
- The one with mediocre Strength and the Athlete feat.
- The one with low Strength, proficiency in Athletics, and the Athlete feat.
Take out the Athlete feat and you have a two-dimensional axis of ability x skill, which is a level of conceptual complexity I can deal with. The fact that Athlete neither requires nor provides proficiency in Athletics really weirds me out.
Similar conceptual overlaps exist with: Alert and Observant and having high Perception; Actor and having high Deception and Diplomacy and Disguise Kit proficiency, and the Assassin's ability to create false identities; Dual Wielder and the two-weapon fighting style; Durable and Tough and having a high Con or being part of a class with large Hit Dice; Great Weapon Master and the great weapon fighting style; Sharpshooter and archery fighting style and being proficient in martial ranged weapons; and there are probably more.
All of these things are MECHANICALLY different and if you slice them fine enough I'm sure we can come up with reasons for the character concepts to differ but it feels artificial and pointless.
2. When there is NOT much conceptual overlap (e.g. Inspiring Leader, Elemental Adept, Lucky) it makes me feel like characters without those feats don't embody the concept. Like if I want to play an inspiring leader, without feats I just get a decent Charisma, and go around leading in an inspiring way. With feats, I feel like I should give up an ASI to get Inspiring Leader or else I'm just not as inspiring as I really could be.
3. Steep cost for marginal benefit: with a few exceptions (Polearm Mastery, maybe the -5/+10 feats or Heavy Armor Mastery at low levels), most feats are not worth giving up +2 to your primary ability score. So now there is the unfun dilemma of: should I make my character weaker, in order to fit my concept and/or get an ability that is more interesting? I don't consider this a fun trade-off. In fact it feels agonizingly painful.
Some people say, "Well your primary stat gets to 20 by 8th level so then you can start taking feats at 12th level." ...But I only want to take a feat if it's important to my character concept, and if it's important to my character concept I don't want to wait until 12 level to get it.
-----
So my objections are mostly around a particular sort of frustration I feel during character-creation. Once game-play starts, or when I am the DM and not a player, feats are not such a big deal, and are largely indistinguishable from class features that happen to span classes. That's why as a DM I allow feats, but I still hate them and think that 5e could have achieved the same level of customizability in better manner.