Rant Warning!
While the Monk class can encompass a wide swath of non-Asian warriors, the fact is, the class has always been very heavily coded and marketed as "Kung Fu Guys", I mean, look at most of the Monk art that's been produced over the years. Or the need for some older editions to add every wacky martial arts "weapon" (sometimes using the term very loosely) to the game!
I remember a Dragon Magazine that offered an alternative Monk, based on African fighting traditions that was pretty cool, but it's a rarity to see official content that says "hey, not all Monks are Bruce Lee!".
Heck, usually when someone tries to make a Brawler or Pugilist, it's a variant Fighter, not Monk.
So DM's who want to allow the class are left with two options. One, have a "fantasy Asia" in their campaign, no matter how distant and far away. Two, go out of their way to create new flavor to support the mechanics of the class (or worse, try to kitbash modifications to the class- in one campaign, I had SmallkinHalfling martial artists who focus on kicking wearing heavy shoes called Klogs, loosely inspired by Savate and Capoeira, and I spent too much time figuring out how the shoes would work as weapons for a "Monk").
I don't mind the Monk (when it's not terrible), but it's designed to mimic one thing accurately, and anything else requires a little squinting or engaging in actual game re-design. It's one of those proud nails in the class system, a class with too much flavor, as opposed to the oatmeal most other classes are.
What's worse is, it doesn't often even work that well with the fantasy it espouses- there's no options for the Monk to learn strange new fighting styles or secret techniques, which is the basis for oh so many martial arts movies!
I remember a B:TAS episode where Batman and his rival, a Ninja, were both searching for a scroll that would teach an instant death move, a great adventure story, but to do that with the Monk, you either have to ad hoc an archetype or a "grandmaster training", when such options should already exist- because let's be honest, not every DM knows what they're doing. They might think "hey, I'll let my Monk learn a Hadoken or Kamehameha move" and only after the fact realize they may have horribly unbalanced the character by doing so.
Bottom line is, if you don't feel the flavor of the Monk "fits" your brand of D&D, don't feel you have to embrace it. Changing the flavor only goes so far, you're still left with the very specific grab bag of supernatural abilities the class offers, even if all you want is to emulate an MMA fighter or it's antiquated equivalent (say, Pankration). Even making a new archetype doesn't eliminate the things that don't fit, they just grant other options.
It's kind of like psionics, but worse. You can ban the Soulknife easily enough. But having to ban a whole class or take it upon yourself to modify it? It really shouldn't come down to that. Even little things like changing the name of "ki" doesn't really do the job.
Heck, most fantasy brawlers can wear armor, for example, something that the monk isn't designed to emulate at all! I saw Jet Li use shields in movies, but monks in D&D don't do that either!
It's ok to not love the Monk. I realize the OP wants to learn to like the Monk more, but you have to do a lot more work to justify the class in your setting than arguably any other.
And before anyone says "it's not that hard/just do X,Y,Z", just keep in mind that few other classes ask you to go out of your way to make room for them.
All you need for Clerics is Gods willing to reward faith. All you need for Barbarians are tough people who live in harsh environments. All you need for Wizards is people who can learn magic from books.
The Monk requires orders of mystic unarmed (kinda...) warriors with specific, set abilities to exist, without any guidelines for how Elven Monks might be different from Dwarven ones, or Centaur, or Plasmoids. Lineages with weapon training should automatically include those as "monk weapons", a lineage that can teleport should have special teleport maneuvers available to them, Dragonborn should have ki-powered breath attacks, ala characters like Dhalsim or Karnov, etc..
Now I can see the argument for this sort of thing to exist for other classes to a degree, but this sort of thing is literally in the core identity of the Monk:
Monks are united in their ability to magically harness the energy that flows in their bodies. Whether channeled as a striking display of combat prowess or a subtler focus of defensive ability and speed, this energy infuses all that a monk does.