Correction, it's a roleplaying game. You are supposed to play the character as if you are him. That's the whole point.
Now, to get back to your original question, what is wrong with balanced encounters?
They break immersion.
If players know each battle will be "balanced", it means they know they stand a good chance of winning since it's more or less guaranteed that it's a straight-up, fair fight. But why should monsters or PCs fight fair, if they want to win? (and live!). Han Solo doesn't fight fair. Darth Vader doesn't either. There is place for Luke and Han in the same universe. Don't make every battle "Luke", in other words two-dimensional.
Monsters should flee and come back when PCs are sleeping and slit their throats, or lock the door to that dungeon room then flip the lever to let the water in and drown them. Those things are not "balanced" in the sense of fair, straight up fights.
The fact that players know you are making encounters they can win, tips your hand.
It breaks immersion, because fairness is something humans try to impose on the world, not something inherent in any remotely reasonable approximation of a fictional world which might indeed plausibly exist. An implausible "fair" world is unbelievable, on its face. It's fake.
A DM shouldn't impose a will to make a fair playground for PCs to level up in, in my opinion.
Players should pick their battles according to which they think they stand a chance of winning. It's not the DM's job to do that. If I had a bunch of 1st level PCs try to attack that group of ogres over there head on, I would let the dice and the rules slaughter them mercilessly. Maybe next time they will know, Ogres = tough. Lots of ogres = we dead. Don't do that again. Lesson learned. Your DM isn't your golden parachute to bail you out of every mess you jump head first into, he's an impartial observer.
By presupposing every fight is balanced, you restrict the wide variety of experience the game can create needlessly. You inflate casual skirmishes to boost up enemy ranks, or make some of those ogres leave. Why? Let players attack when they have overwhelming odds and a great chance of winning (smart game play, it's a game, right? So let them play. And learn by failing), and avoid battles where there is a substantial risk of death or loss. That's pretty obvious.
Balanced encounters are the bane of immersion, they are a terrible invention if you want to maintain player focus and the illusion of an independently existing and populated world, full of mystery and danger and excitement. Balance is the opposite of danger, it's forcing a level of fairness on battles which doesn't belong there.
you know what a sport and D&D combat have in common... they are both games...
D&D is not a sport. But even sports have rules, and you aren't supposed to cheat to make sure one side wins every time.
And yes, D&D is a game. A roleplaying game. Meaning immersion and the suspension of disbelief not only matter, they are actually of central importance. Reducing D&D combat to a sports contest trivialized any danger it might have. Which is not only bad for immersion, I don't think it's fun to play a game I know I'm going to win every time. It's like playing chess with your kid sister. Winning every time, yay. So exciting. I can't wait to see the surprise in store for next time I play. Oh wait, I won, again?
unless you are playing a legendary hero... or really any tv show or book protagonist (well ones not written by martin)
Early D&D was very much closer to Martin than Tolkien in effect. Players are not guaranteed to become heroes with the invisible hand of The Author ensuring them safe passage back from the slopes of Mount Doom. The dice are there to make sure the outcome of the game is uncertain, even a total loss is a distinct possibility. That's what makes D&D great.
Combat as sport trivializes battle and only comes about in games where it's difficult to die, to the point that every possible chance for battle will be taken, again, since players know they're supposed to be "balanced" in other words winnable in a straight fight. Those two things go hand in hand, and both contribute to wrecking immersion, the feeling of danger, and thereby the sense of actual accomplishment and the thrill of victory.
that's pretty close to what I want... let me explain.
I want I good story and I want it to feel hard pressed and earned, but the secret is... I want the PCs to win...everytime. They don't, they win they loose, sometimes PCs die. But I am hopeing they pull it off everytime. I am disappointed when a PC dies (although I don't pull my punches) and happy when they win. I do my best to make every victory worth it...
it's a game it is as much in common with warfare as HE-MAN, or Yu-Gi-OH, or Batman, or Hercules the legendary Journey, or JEM....
that is pretty much how I start every campaign... but I still make sure they numbers balance so they can still win...
There is no real difference between making sure the maths work out so the players always win statistically, and just playing a story game without dice. You are removing the agency of dice from the game, silencing their voice. If the maths are manipulated behind the scenes so every battle is an expected win, players won't think of running, they won't try to think of other ways to win than fighting, or of avoiding battle at all. You are actually restricting gameplay, since players see combat as sport, and are sportsmen (and women), and those games are fixed.
It's funny that on the one hand you see nothing wrong with combat as sport, but on the other hand, you admit that you skew the math so the outcome is favorable. This is the D&D equivalent of deflating the monster's balls (although that does, sometimes, literally happen. Ha).
2e, 2e w/ combat and tactics and skills and power, 3e, 3.5, pathfinder, 4e, 5e, rifts, deadlands, savage world, gurps... all of them I play the same way... and run the same way... I assume the PCs will win more often then not and am secretly chairleading that victory 99% of the time...
When players know that, they lose fear of the world, and that destroys immersion and suspense. How can there be suspense when the dice don't matter? Where is the thrill, the surprise in that? You are playing a game of D&D that is founded on dice, and it seems to me like you don't actually want the dice to have any real significance to the outcome of the plot. Or if they do, you want to minimize it to such an extent that you might as well be playing a diceless game.
Conan is a great example. If one person in your group rolls Conan stats, does that preclude you adventuring with them? Maybe Conan is indeed the 18 18 18 8 8 8 min maxer's dreamboat, so what? That still leaves plenty of place in the game for a voice or reason, for a magician to guide his uncouth ways, or to help him sneak into the palace. I seem to remember every one of his movies he had allies that weren't as tough as he was, but they still contributed and shored up his weaknesses. If I was in a party with such a person, and I was playing a wizard with a 14 int, that's still a huge improvement.
Even making a second warrior, a dex-based one, with a 14 in dex, could at first level still have the same to-hit as Conan does, with his three natural 18s in the physical stats. As I wrote before, you pick a human variant, with archer style, and sharpshooter, and wear chainmail. There, 16 AC, two attacks per round, at +6 each. or +1 each when using sharpshooter. You would definitely be giving him a run for his money in the DPR department.
And I could play a 14 int wizard that contributes just fine, it's more about the intelligence of the player than the PC.
I think he doesn't believe in odds and hates when people quote them... 
