Sometimes you win, sometimes you lose. But forcing a player to accept a loss is never fun, and the point of any game is fun. You don't want your tanks sitting around with less health than the mage, and you don't want your mage to have more strength than the fighters.
Which is why I closely supervise rolling when I run a group that I allow rolling. 7 sets of 4d6, re-roll anything lower than an 8. Yes, i'm fairly generous to my players, and sometimes they can be a little OP, but 9/10 times, people are happier with stronger characters than weaker ones. And adding more enemies, making those enemies stronger, has never been a bother for me.
I would rather have to tune up a game to handle OP characters, than tune it down for weaker ones. IMO, players are quick to sense when they are very weak, and the challenge really shouldn't be a challenge.
If they do not want to roll on day one(I prefer having a "character making session" day before the game), then it's the point buy system. Sorry honor system, can't trust you.
Personally when making characters, I prefer a point-buy system. It avoids "honor system" and "good/bad rolls" drama, and it's easier to balance games around.
Personally, if I rolled stats and was gimped across the board(say, three 8's, one below, and nothing above a 12), I'd ask for a re-roll(unless everyone had similar stats), because lets face it, you're not going to do much of anything in any game with those kinds of numbers without the GM having to REALLY adjust things for you.