The problem with your argument is that a few stat bonuses (+/-5% to 15%) isn't substantial enough to be noticed, at least not in the manner that your analogy suggests. It certainly isn't 99% at all. +1, +2, +3 are not equal to 99%.
In addition, a character is more than his stat bonuses. Characters should be persons first and foremost, interacting and role playing have little to do with rolling dice. So for a large percentage of the time during the game those bonuses are not going to overshadow the game.
I disagree, stats can make a huge difference in characters. Let's say my wife and I want to play Tik (short for Tika) and Tok, dwarven fighter brother and sister. We're going to be the front line for the group, but we also want to synergize our capabilities and discuss in combat strategies (like taking defensive fighting style to protect each other) and feats (do both of us need to take shield master, or just one). We also discuss out of combat options like Tik being the kid that always took things apart just to put them back together (good with thieves tools and traps, a backup rogue) and Tok was always trying to smooth ruffled feathers when people were the victim of her traps so he's quite persuasive and may be able to tell a fib or two.
Ok, cool. We have our character concepts and we go to roll. I roll well (similar to another player in the last game we rolled for stats) and get 2 18s and no stat below 14. My wife rolls poorly (also similar to last game we rolled for stats) and gets a high stat of 14, a 10 and everything else below.
Suddenly Tok does 65% more damage, and can take 20% more damage than Tik. Tok has no problem being one fo the more charismatic members of the group and while he's at it he can have some other out of combat skill. Tik? Well, she had to put her 14 in strength, 10 in con, so she's going to have a negative to those thieves tools. In addition, she's not very wise, intelligent or charismatic. Tik's saving throws also suck, while Tok is sitting pretty.
We could switch Tik over to be a mediocre rogue, but then we don't have a second front line fighter that the group needs. Oh, and dwarf is not a great race for synergy with a rogue (especially with such low stats) so she should switch races as well. Suddenly the vision falls apart.
Finally, to say that these 2 are "close in capability" from a metagame standpoint is laughable. These characters do not fit the vision we had for the characters. They can't contribute (numerically) on an
even footing outside of combat either. Tok will always be better than Tik from a numerical perspective or have access to more feats.
If you like random results, that's fine. Just be willing to own up to the results.
I was going from memory on extra damage and so on and goofed.
Assuming target AC 13 (average)
Both using battle axe, average damage 4.5 per hit
Tik: Strength 16, has +4 to hit, 7.5 damage for average (.45 * 7.5) = 3.375
Tok: Strength 20, has +6 to hit, 9.5 damage for average (.55 * 9.5) = 5.225
Tok does 65% more damage per round.
Tik has 12 HP, Tok as 15, Tok will last 20% longer in combat, not considering his far better saves for pretty much everything.