Now this is gonna be a wall of text, because I am trying to explain as much and as clearly as I can here. Just as a heads up.
TLDR: Off the chart stat is just as OP as overloaded kits, no one is more acceptable than the other.
it's determined by your skill.
"Yeah because I play X champ longer, I am automatically entitled to access superior champs." - OP.
It's like saying in a fighting game you should get access to characters with way longer potential combo chains, nonexistent recovery time and infinite lock downs because they are harder to get used to. Or how say in FPS, you should be granted more kill streak bonuses because you use a gun that is harder to get around. Those designs are unfair and broken, it's simple as that.
Things don't have to 1 shot you instantly with no chance for retaliation or tanking 5 people while refusing to die to be considered OP. Because kit size, spammability and versatility are still a part of the consideration towards a champ's actual power.
Saying an armoured man with a shotgun is OP, while turning a blind eye to a man with knives, assault rifle, pistols, submachine guns, grenades and whatnot in his coat all at the same time when everyone is only allowed to keep only a main weapon, a sub weapon and an extra tool is hypocritical.
Yeah it does take skill for the latter to get access to all the benefits he has but that doesn't mean he didn't break the rule nor is he somehow not OP. It's not the kit's fault if you lose while using a larger kit because you're too busy trying to show off (which is how most overloaded champs lose in this game), it is however, the kit's fault when you've mastered the said champ and just offer plainly way more than everybody else on the roster because you do more, with minimal amount of drawbacks due to how versatile/flexible your champ is by default.
**
The keywords here are versatility, flexibility and choice.** The advantage of being overloaded is already there, the flexibility. Overloaded champs are immune to meta shifts, nor are they a subject to counterpicking and counterplaying, their only enemy is their own player's incapability and time itself which is already toxic enough of a design. But people (including Riot) have the gut to come out say that "hey but you need more skill so you should be rewarded more"?
Well, indeed, they should. BUT there is a limit on that, and LoL clearly does NOT have the limit set, judging by the extreme gap between champ pick rates which can range from 0 point something to 20-30%. There is no one who can look at that stat and say "this game is balanced" because then you might as well buy yourself a pair of sunglasses and glue them onto your face.
"High risk high reward" is not a self imposed limitation on the player's part, it is and should be a part of the champ's design. The difference between the good o' Master Yi and say a Zed is that Yi is the latter while Zed is the former. Zed DOES NOT have to be flashy to be effective, Yi HAS TO rek everybody with his limited kit to be effective later on in the game. Zed has a lot of choice, Yi doesn't. And that marks the difference between a healthy champ and the otherwise as too much choice is just the same as too much power unless you do exactly 0 damage and dies in 1 hit then nobody can help you.
Would you rather have champs that is not balanced in low elo because no one is actually good there so people get stomped all the time, or have unbalanced champs in high elo meaning the game itself isn't actually close to being balanced?
LoL is the latter in the above rhetoric, and that's really bad. There is no excuse to justify the blatant awkward balance policy where more versatile champs should also have roughly the same amount of actual power as everybody else, of course they dominate the pro scenes and outshines the other specialists (who are restrained by their kit) like no tomorrow. What a surprise I should say.
As a final side note, I am frankly quite sick and tired of seeing people who conveniently ignores pick rates and other balance aspects such as items and solely look at the champ's win rate to decide the strength of the said champ.
Learn basic statistics. I am no mathematician nor do I have the capability to, but even then the stupid me understands how other factors skew the win rate in different ways. Come on.