I mostly go the other way -- it goes too much against my intuition to have someone who is only "average" in the most important attribute for a profession be almost as good as someone, all else being equal, who is a paragon. Flyweights should be pounded by heavy weights, people of average dexterity shouldn't almost qualify for the Olympics in gymnastics, and it seems reasonable to me that people of average intellect should reach their limit in math long before they get close to the PhD level classes.
The real problem is that skills and stats can't easily be codified. Is that heavy weight good because he's strong or strong because he boxes all the time? Is that gymnast good at acrobatics because they are dexterous or are they dexterous because they spend all day stretching and practicing acrobatics? And is "being dexterous" in terms of being good at acrobatics really the same as "being dexterous" in terms of manual dexterity such as picking locks? Could it be that the gymnast who appears to be dexterous is simply countering her lack of natural dexterity with an overwhelming amount of skill? If she were put into another environment that required dexterity (such as archery) would she immediately be great at it?
I kind of dislike stats as anything other than a role playing thing because of that. The best fencers in the world don't have Arnold Schwartzenegger sized muscles to be able to hit better. Strength should mostly be a damage thing.
I think skill should matter more than stats. A really skilled mountain climber likely has some upper body strength. But it's likely nowhere near that of a championship weight lifter. Though I would suspect the weight lifter would be worse at climbing if he's never been before. I think if a skill is going to give you +3, a stat should never give you more than +2.
Another solution is to just force all the PCs to be average... which means they're adventurers in a world where about 1/4 of the population is noticeably better suited for adventuring than they are (except in temperament) . That just seems odd... especially if its coupled with no ability increases.
I generally assume average stats(ie all 10s) for all NPCs except where there's a notable reason that someone needs more than that. Sure, there is a periodic smart person or strong person, but they are rare. Generally, I assume that the dice don't determine the actual odds of having that stat for NPCs. Instead it should be something like 50% of people are 10 or below in a stat. Then the rest of the numbers are split in half each stat increase(25% have an 11 in that stat, 12.5% have a 12, 6.25% have a 13, and so on). The dice are just for the players.
As for stat increases. I'd much rather a system where becoming good at a skill raised the associated stat slightly. Train in climbing? You are bound to acquire some strength. Train in acrobatics? You get more dexterous. But only up to a limit. And frankly, it should take longer to go up the closer you are to the limit.
I think a lot of types of gamers will do this anyway. But why shouldn't someone whose character conception is a not-to-bright, socially inept, fighter trying to fit into the world min-max to rock in pure combat? Say they do... if you want your character to be smart, quick, and charismatic, why should you also get to be almost as good at beating people up?
Because, in my experience combat is 90% of the game. And even when it doesnt take that much time, combat is more important since it is often life or death. Whereas quick and smart is a role playing choice mostly for flavor. There are quick and smart ways of killing people that are just as effective as brute force ways.
The game gets very frustrating for people when it proceeds like this:
Player 1: I outsmart the guy at the store and charm him to giving us a discount. I'm really good at that.
DM: Alright, you get your supplies and head out on your expedition to the cavern of certain doom. Along the way, you run into an ogre. It swings at Player 1 and does 20 damage.
Player 1: Umm, I'm dead.
Player 2: Really? Cause I have 20 hitpoints from just my Con modifier for 4 levels. Oh well, I swing at the monster doing 25 damage to it. It dies. That was easy.
Player 1: For you, maybe.
One of my favorite things with character generation has been when the DM has said "make your character idea and pick the stats that fit it". In the current 1e game I'm in, I think only one of the characters has a score above 16 (and so virtually no one thought it was important to have many the large bonuses, even when we were free to take them). In a VtM game that used this system the GM just used other aspects of the game to balance out what we chose.
Well, it must be nice to play with those kind of players. I can tell you if I told my players to do that, they'd have at least two 18s each.
Though, my original point was that in 1e stats mattered less. If we were playing 1e, it's likely that almost no one would take 18s, since they didn't give you much. Con modifiers were nearly useless to you if you weren't a fighter, strength didn't become very useful unless you were a fighter, and most of the other stats didn't do much of anything.
As for VtM, if you are referring to using "other aspects" to mean using role playing disadvantages to cancel out combat benefits, I can tell you it rarely works. I ran a game of 2e using skills and powers once(where it let you separate your stats into two substats and choose which stat bonuses you got. Plus you could take disadvantages like "antisocial" in exchange for using d12s for hitpoints instead of d10s). I thought it was great because it let people customize their characters exactly how they wanted them. A friend of mine said it was really dumb and set out to prove it. He took nearly every social and role playing disadvantage in the book and bought nearly every combat benefit he could find. Then he rolled stats over and over again, each time claiming that his character immediately committed suicide if he stats weren't good enough.
The game started when he went into the bar and immediately started pissing off everyone in it with his personality quirks. He eventually started a bar fight, and killed each and every person who attacked him(he didn't know how to hold back, one of the disadvantages that got him the points). Eventually guards showed up to stop him. He beat them soundly and took their stuff, making him even better. So I threw better guards at him. He beat them, took their stuff and went up a level. I told him I'd eventually beat him by using enemies 10 or so levels above him. He agreed but pointed out that his disadvantages hadn't made the game any more fun to run(he wouldn't have started the bar fight, but his disadvantages made him) and he was able to fight enemies designed for entire parties of 5th level characters solo since he had all the extra combat ability. I'd kill him eventually, but then the game would be over and no one would have had any fun.
The same thing happened with the 2e thief kit Swashbuckler that gave you the thac0 of a fighter and some more combat benefits in exchange for "trouble finding you more often". Half the time the DM had a plot planned and didn't have room for adding "extra trouble" just because someone chose the kit. The other half of the time, the player loved it, because the plot revolved around him, he got more "screen time" and often got more xp and treasure for fighting off the trouble.
We eventually agreed that choosing to act like an idiot shouldn't give you combat benefits whether it was due to a disadvantage system or simply because "big, dumb barbarian" was your role playing concept.