The best character creation systems combine a level of chance and a level of control. All control with no chance leaves no room for ideas that fit outside the limited possibilities allowed, while total chance may leave you with something you have no interest in playing.
I agree with this, but in the context of D&D, I can think of no system that meets the competing criteria. I'd love to have one, and I've been racking my brain on and off over the problem for nearly 20 years now. If you've got a good solution, I'll happy gives you 20-30 XP for it.
Take any random system that you want. Whatever results that random system produces could be exactly replicated by some system where the DM randomly generates a stack of points for each player to spend, and then the player spends his allocation of points to create a character. And as a thought experiment, I think that shows why its very difficult to create a random system that avoids problems. What we'd actually want is a system that is both random, but always generates a fair and balanced result so that everyone is on as level of a playing field as we could manage, and which is random but over which the player had a certain level of guidance so that it doesn't produce a character which he has no desire to play.
That ideal system just simply may not be possible. The goals are in too much competition.
The best I've been able to come up with is start with any point buy system. In theory, what we could do is begin to randomly assign values until we had assigned as many benefits as hit some point buy value. So in the context of say 3e D&D, we could randomly select an ability, and randomly generate a score for it. Then we could compute the number of points that have so far been spent. Then we could randomly select an unfilled ability, and randomly generate a score for it. Continue this process until there are no more points left to spend, at which point the remaining scores are all bought at the '0' level, or until there are enough surplus points remaining to buy the last ability (or abilities) at some value.
That's not terribly bad, but it does have the subtle problem that all point buy tends to have, and that is that not only is point buy often not perfectly balanced (some abilities in D&D tend to be better than others, for example no one wants to dump stat CON), but point buy tends to neglect the value of synergies that players don't neglect when spending the points themselves. For example, DEX synergizes well with INT, because rogues who would prefer a high DEX score, also would like to have a high INT score, and Wizards - who need a high intelligence score - would prefer a high DEX score. It might not synergize as well with a high WIS score, because the natural use of a high WIS score - make a cleric - doesn't get a huge benefit from a good DEX, pushing you toward some less intuitive and perhaps less potent builds to get a benefit from both.
The more complex your point buy and the more parts of it you want to make random, the more that is true. For example, if we randomly assigned ability scores in D&D, and randomly assigned a class (or randomly generated a class), then invariably we'd generate more characters where the points came out at the desired total, but the synergies weren't there.
When rolling, what tends to happen is that we recognize that random is problematic, but don't want to give up the sensation we feel when rolling the ability scores. We want to retain that thrill of victory, but we don't want to retain the agony of defeat. So we come up with methods that are like gambling, but with free insurance. We gamble, but if we lose, we can play again without paying a cost. So we end up with a system where we can't lose, but have retained the sensation of gambling.