Totally didn't read the thread. Just hopped on, read some of the posts, but not a lot of them, figured I'd throw my opinion in.
Munchkin - A combat twink, cares little for the game itself, only seeks to be the most powerful creature, "My fiendish half-red-dragon troll weretiger took a few levels in monk so now I flurry for 5 attacks in a round, count as a magical weapon, and my claws deal a base d8, picked up rogue to throw skill points into control shape skill and sneak attack oh and I'm basically immune to everything but acid damage over 10 points and being banished since I'm an outsider... Backstory? Uh..... Fiendish Troll mated with a red dragon natural weretiger? I dunno man, it's awesome and practically can't die. Oh, I'm ALWAYS in hybrid form."
Power Gamer - Key distinction, gamer, wants to make the most powerful CHARACTER they can, "I am the most powerful wizard the world has ever seen!" "I am the greatest swordsman in all the planes!" "I am the greatest thief to have ever lived!" Yes, they still use munchkin combos and tactics, but it's to serve an end a character would have, sure the motivations are usually the same as your cliche villains, but at least they exist and are thematic.
Optimizer - They have a character concept, and they want to be effective at what their character would do; "Ok, so I'm playing a noble knight kind of character, I like action surge and second wind, so I'll pick up two levels of fighter and grab the extra fighting style to pump ac, but then I'm going straight paladin from then on out so that I can get aura of protection and have insurmountable saves."
"Average" Player - not actually the average player, my experience bares out the 80% combat junkie estimate someone made earlier, but conceptually the average between "make it broke or gtfo" and "gimp my character and I'll play the DM instead, ultra-rp" player types. They will be the ones making your Gokus and Narutos and He-Mans and Legolases and Striders and so on. They'll grab something they think is powerful and use it when they can, but otherwise it's about having fun and being pretty close to what works for the game and what works for the character.
The Role Player - Totally built for the character, options are what a character who does not actually regularly adventure would take, "Well my character is a cloistered scholar type, so my 1st level spells are find familiar and unseen servant, with mage hand, mending, prestidigitation, and message for cantrips." Not that they're ineffective, they do take good esoteric skills with good potential for utility in RP and exploration, they just are playing a character that doesn't really think of themselves as an adventurer per se, but rather a person who is going on an adventure for some reason.
The Social Engineer - Intentionally gimps their character and builds "suboptimally" but it's not actually suboptimal in the sense that they intend these choices to be effective, but not in the traditional mechanical view of effective, "I have my unseen servant pull the knot on the chandelier above the duke and his men as they threaten us." They take spells that optmizers and munchkins and power-gamers normally turn their noses at and try to use them in ways one wouldn't normally expect, trying to play the DM rather than the system.
I really feel that, fundamentally, both the RP nerd (trying to think of a similarly pejorative way to say this as munchkin is typically used pejoratively) and the munchkin are the same person are just different manifestations of the same kind of mindset, "I'm going to find a way to beat the game" with the munchkins looking to exploit all the rules of the system and rp nerds seek to exploit rule 0.
However, I feel that a "everything balances out in the end" kind of system wouldn't allow players to feel like they could genuinely take part in a world they could believe. Consider; is a handgun balanced compared to a fist, a high-caliber long range rifle balanced to a hand gun, a drone balanced to a high-powered rifle, so on and so forth. The world we actually exist in isn't balanced, and so to make a system so disjointed from reality (the mop and katana objection for example) breaks immersion for a lot of people. Think about it like this; in an all-balanced system the player who makes a character that wields powerful magic is going to be dissatisfied when the guy sitting next to him makes a ninja that wields chopsticks (surf ninjas anyone?) who is just as effective as him in combat. "But the magic user will have out of combat abilities thanks to magic that make him useful there" is easily countered by "and so would the ninja that uses chopsticks." In this hypothetical system, each class would need three categories of abilities; social, combat, exploration. martial types would have intimidation and feat performance social abilities, while casters and charlatans would focus more on being silver-tongued, martials are going to focus on reacting quickly and movement options, casters and charlatans will focus on detection and avoidance, and then all the varying combat options of course. It's not that power-gamers and optimizers are going to be dissatisfied because they can't be powerful, per se, but rather what they think should be powerful won't be.
So, for instance, the mage casts fly and flies over the castle wall with impressive magic, the ninja puts on some climbing claws and scurries up the wall. Both characters have options for overcoming pretty much any obstacle, and so there is no benefit for having sacrificed option x for option y. Why bother worrying about components and being able to cast or anything like that, when I can just play a mundane that requires a few common nonmagical items to accomplish the same thing?
Think about it from the perspective of other systems too; shadowrun is a good one, do I go ultra uber magic, barely human cybernetic organism, or the equipment monkey that has a gadget or gun for every conceivable situation? What makes this system so good is that you can be awesome with any avenue, but at a cost. If you go full magic, you're not gonna have a good time with implants and artificial limbs, if you go artificial limbs you can just forget about magic, and if you're an equipment junkie you can kinda sorta dabble a bit in both but your credits are tied up in guns, ammo, and toys so you're not going to, outside of storyteller intervention, have the funds and resources to invest in either one while maintaining a diverse and useful inventory. Or world of darkness vampires; unless you're eating vampires left and right in some sabbat game gone horribly, horribly wrong, your choices have consequences that also come with some benefits. You can absolutely play a social nosferatu, but you'll want to invest in a lot of obfuscate. A mental brujah? Bruh, celerity is the great equalizer in physical combat. A physical tremere? Dude, I shouldn't even need to give an example, thaumaturgy was kind of a bit broken lol in 2eR.
The point I'm trying to get at is in a system where things are generally balanced out there aren't going to be real drawbacks, and it won't be realistic. Life isn't fair. It's just not. Being strong is going to get you a lot farther than being able to take a baseball bat to the face as being intelligent is better than being wise because knowing how to do things is objectively more useful than knowing why to do things, and let's not even talk about appearance versus personality, the world around us all is evidence of the disparity between attractiveness and likability (Kim Kardashian, rest my case). If there's no ACTUAL drawback to my choosing to be a chop-stick wielding ninja rather than a magic slinging wizard, then why not play a bare-knuckle boxing technomancer?
Balance is good, don't get me wrong, but a lot of balance, in my opinion, is the drawbacks associated with the benefit. A gish build that is good in melee and magic is probably going to be lacking social and exploration options, and a utili-bard is probably not going to pump out damage like a great weapon fighting smite-monster paladin but if you need to know something or talk somebody into or out of something they are your guy. If you want to undertake such an endeavor, I think you'll find providing drawbacks for objectively more powerful options is going to get you better results than trying to average efficacy between all potential options. Make stuff that is objectively more powerful, just make sure it can backfire or is situational.
Sorry for the long-ass post by the by, and if I'm reiterating points others have already made, I apologize.