I sometimes think part of the divide between random versus point buy/array is the different approach people take to character creation. I hear people saying they want to be "surprised" by their PC. Me? I come up with an idea for a PC that I want to play that will fit in well with the group and then I come up with a backstory. Ability scores are about the last thing I do. Sometimes the stats will be a bit min-maxed, sometimes they'll be more balanced because I don't want to focus on just one aspect of my PC such as combat. But I want to play Mouse the halfling rogue who is intelligent, wise, charismatic and a decent rogue as well. Maybe I want to play Gragnar the Barbarian and min max a bit. I want my ability scores to fit the image I have in my head.
The other aspect I simply don't understand is the thrill some people get from the gamble of rolling for ability scores. Maybe that's because I suck at games of chance. I went to Vegas once and, because everyone else was gambling, I put $50 into my pocket. I figured if I ever got to $60 I'd quit but otherwise I'd just put all my winnings back into my pocket until I ran out. Even though I've been told that it's highly statistically unlikely, I never put any money back in my pocket. I played twice on a $5 machine, everything else was dollars or quarters. I would have killed myself with boredom losing all that money at nickel slots so I didn't bother.
But determining ability scores for my PC takes, what 10-15 minutes? The thrill of rolling is supposed to justify playing with that PC for months on end is supposed to be enough to justify the risk of having crappy ability scores? Nah, not for me.
I would actually be fine with randomly-assigned and generated ability scores as long as they were restricted to fall within the range of what you'd get from point buy (like that site linked above does). It's not the randomness that bothers me, it's the intra-party inequity.
And "life isn't fair" isn't a convincing argument for me. I'm not DMing in order to teach unflinching life lessons.
The part I don't understand is what seem to me like very elaborate, baroque ways people use to arrive at their scores (rolling and sorting through multiple sets, stat drafts, etc). To me that stuff seems like a huge waste of time to arrive at a result that is very, very similar to point buy or standard array. But the answer is clearly that some people just really enjoy doing that, so have at it.