I'm one of those who strongly prefers rolling. I prefer it because it creates more varied character stats. With point buy, you can't have anything lower than an 8 or anything higher than a15 (before racials) - and that's just plain boring. If you play a lot, then every stat line begins to feel samish... which may explain some of the complaints I've seen from point-buy enthusiasts about 5e character stats always feeling like they're starting in the same place. Of course they do, if you're all using point buy.
Personally, I love having a margin between 3 and 18 per stat. That's a wide bracket, and that makes for interesting dynamics. I *love* having a 5 or a 6 - which I can't do with array or point buy.
I've used versions of point buy that let you buy down as far as 6 (gaining points back on the same scale) and up as far as 16, and I've got less objection to that, but I still prefer to roll, as do literally all of my D&D friends, across 5 games.
I've never 'not rolled well enough' to pull off a character concept; regarldess of what concept I'm running with, rolling lets me do it, because your character is low level - so what they're 'good' at is relative; your best doesn't need to be best in the realm. I've had more problems with putting the strongest two rolls in their strongest attribute, and then being stumped because all of my remaining values are *higher* than I want for the stats that remain. Last time I made a character, I had to ask my DM if I could trade out a 12 for a 7, because otherwise I'd have had no negatives at all.
End of the day, we need the right to chose which derivation method we want to use, because people will continue to have strong options about this... so unless you give us the three main options to pick from, folks are going to be unhappy.