I don't consider 'I want to be a standard X, but in addition be really good at Y without having to pay the costs normally associated with it' to be a legitimate "concept" for a character - in general "I just want to do more, and do it better, and not have to give anything up" isn't what I file as 'character concept'.
Not have to give anything up? Have you tried to play a grappling monk? We have a ruleset entirely set up to use an ability score that monks almost never use because its entirely opposite from the ability score for which the game has assigned to the monk as its primary ability. If you "follow the rules" as they are currently written, you can get the style of character you wish to play, but that character will be noticeably WORSE than if you just played a bog-standard monk. So allowing this one character to use DEX (Acrobatics) to grapple rather than STR (Athletics) is yes, "getting something for free"... but that's only because the cost of it is so exorbinate that no one was ever going to pay for it in the first place. And guess what? The monk who is now grappling with DEX is still going to to be overshadowed in many ways by the fighter player who takes Great Weapon Master and all the other "real rules" to make their character. So getting stuff "for free" does not actually mean all that much when all it does is just keep the character viable.
I doubt I would enjoy your game, because for me part of the fun of playing D&D is the challenge of making an effective character and fighting monsters within the rules of the game. Claiming that someone is 'hung up on the idea' of actually playing a game using rules when that's the central appeal of playing a game to them is using the rules is not reasonable; it's like claiming that someone needs to get over their hangups if you're playing chess and they start moving the bishop horizontally. Painting people as 'hung up' and 'unable to handle' if their interest in the game is actually dealing with the rules is simply unfair to them.
See... I believe this is a false argument. Here's why:
When the Sword Coast Adventurer's Guide or Xanathar's Guide came out, did you or anyone else in your game make a character that used any part of those rules? If so... then you are doing exactly what I am, only you
believe you are not.
The rules of D&D for the longest time were what was in the Player's Handbook. Those were the rules you were using. You wanted to play "by the rules"... and you did. Which is great! You got what you wanted. But then SCAG came out and introduced the Bladesinger. So now... a character concept that up until that point was not very well realized-- the wizard who can also use a blade somewhat effectively-- could now be played because someone decided
to change the rules.
Was that someone Wizards of the Coast? Sure. But it doesn't change the fact that the rules of your game were broken, and you now had wizard players "getting something for free" that they hadn't gotten before. Before, a wizard would have had to take a level of fighter and push some of their spellcasting back. But now they didn't have to. Someone broken the rules of the Player's Handbook so that a person could play this specialized character concept more effectivdly now than they could before this subclass was released.
But I'm pretty sure you didn't see this as something "wrong" right? Since they were the designers of the original rules, they could break them all they wanted, but you could tell yourself that they weren't. They weren't breaking the rules, they were "expanding" them.
Nope, sorry... they were breaking their own rules for their player's benefit. Just as much as every single one of the rest of us are... every time we create a new subclass, or let an Arcana domain cleric use INT as their primary ability score, or let a rogue Sneak Attack with a club. All to help fill in gaps in the rules which do not currently get covered, and whose actions result in
no appreciable difference in the game other than the player thinking they get to play this cool concept idea.
That rogue player wanted to play a "thug" type of character and wanted to be able to blackjack people over the head. So you the DM let them "get something for free" by letting them use Sneak Attack with clubs and maces... resulting in this rogue still doing less damage than the bog-standard rogue who uses a rapier. Boy, you're a monster, letting this rogue get away with something like that. What are the other players in the group going to think?
I don't understand why you'd play a rules-heavy game centered around classed characters like D&D, but also sometimes run it like a rules-light game. If you want to play a game where you just do whatever and sometimes roll funny dice, why are you bothering with D&D books in the first place?
Simple. I know the rules of D&D backwards and forwards, my players enjoy both the rules of D&D and the "essence" and "story" of the game and world of D&D, and there is a LOT of variation in the rules to make lots of different types of characters.
But the rules do not let you make ALL the types of characters. They aren't that comprehensive. Which is why I feel perfectly fine in giving players what they mostly want by tweaking the rules and abilities so that they can get closer to what they want while remaining relatively on par with the rest of the members of the group.
Could I play all my games using FATE? Sure, if I wanted to. But that's the thing... I don't find any reason to switch games purely in order to keep the rules of any game "pure". "Rules purity" in any RPG I think is dumb. Why hamstring myself by avoiding playing certain games just because of this ludicrous idea that changing/adapting the rules of any game shouldn't be done?
"Why play D&D if you're only going to change the rules?"
Why NOT play D&D if I'm going to change the rules? If changing the rules is good enough for WotC every time they release a new sourcebook, it's good enough for me!