Arial Black
Adventurer
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.
Try rolling stats in order (using whatever system you want: 3d6, 4d6k3, whatever). Now, this is random and gives the player no control. But after rolling six ability scores in order, pick two and swap them over!
You can't allocate all six scores, therefore you get surprises. But you can make sure that your best roll goes in the stat you want. It allows some customisation, but retains the element of surprise totally missing from point-buy.
When you see those six rolls in order, then your only choice is which two scores to swap. That might not seem much, but how many possibilities is that?
Looking at the array you rolled, and mulling over the possibilities, gives you ideas that you cannot get in a system where you had total control from the start. Point-buy allows you to metaphorically make your PC more stupid so that he is stronger. If you want a PC with high Str and aren't bothered with Int, why would you ever choose to have Str 14 and Int 10 when you could have Str 15 and Int 8, knowing that you have two racial +1 bonuses to assign? Thus, the evolutionary pressure for a population of 16s and 8s, with a dearth of (statistically more common) 10s and 11s.
Using this 'roll in order, swap one pair' method, your wizard might be strong or charismatic or whatever.
I imagine a university for student wizards. Each is likely to have high intelligence or they wouldn't have passed the exam to get in! But can we really say anything about what their other stats would be? Some people are charismatic or strong or what-have-you, and these people are randomly scattered among the population, including that university for wizards! This method much more accurately models that likely student population, because you can make sure that your Int is good enough by swapping a good roll into Int if it isn't good enough already, but four out of five of the others will be random.
But what about that same university using point-buy? What, every single one has Str 8 and Int 16? Really? Have you been to a university? Was every single student on the same course equally weak? Equally un-charismatic?
That's one of the reasons that I absolutely loath point-buy. It might be 'realistic' for heroes to have higher than average ability scores, but not that each member of each class to have identical scores.