I had a thread running here a while ago, about character generation and random race selection and random ability score generation. I think that a lot of the problems arise from the fact that you can pick what race you play

Indeed, I have my players roll their race, and then roll their ability scores and they get what they get in the order that they are rolled. Haha, I know, heresy
After, you pick your class. Now, you might well assign your ability score bonuses, if you have some flexibility, knowing what class you'll now be going for. But that's fine.
This idea actually comes from Dungeon Crawl Classics (DCC) where you roll for everything except alignment, your name, and your class (that you choose after levelling up once).
This is actually a lot of fun. Players do not get to pick their race and do a character concept that they have in mind; but you know what? They roll with it. They come up with their character concept after they roll for race and abilities. "Let's see what nature gave me..."
My entire character generation method is as follows:
1) You are born: Roll for race.
2) Natural selection: roll two ability score arrays: each has 3d6 six times assigned in the order they are rolled. Pick the one you like best. (Perhaps you had a brother that died, or lived but never made it as an adventurer?)
3) training: change one ability score of your choice to 14
4) nobody's perfect (and those that are, pay for it): if you don't have at least one score of 7 or less, or two scores of 9 or less: lower one ability score to 6 or less. (Perhaps you had an accident?)
5) pick your class
Makes for a slightly more gritty and variable method. Some characters are weaker, some are stronger. My games are a lot about role-play, typically with 1-2 battles in a given session, so honestly PCs that suck in their ability scores have ample space to shine in-game. Weak characters are often the center of attention for some reason.