And if the ref says, "Would you like to re-roll your hp?"
Who wouldn't?
I'm just saying that, if everybody agreed to play RAW, there are many players out there who might consider themselves roleplayers who would balk at playing a 1st level fighter with 1 HP, probably citing that they can't have fun with such a character.
I think the roleplayer, who would probably prefer to have more HP, would take on the challenge of playing the character as he was rolled and have a good chance of making him a memorable character--maybe even a great personality in the game.
To me, that's the difference in a roleplayer and a rollplayer.
Everybody likes good stats. The mechanical benefits in the game are obvious. I am always suspicious of those that can't seem to have fun, though, unless they have superior stats. You know who I'm talking about: The player who rolls 9-12-11-10-13-10 for stats then whines about it.
Forget the stats. Play a character.
Admittedly, "Play - but don't get too attached," is a good mantra for most RPG characters.
Players who gert "too attached" to their characters is, indeed, a double edged sword.
I love it when players love their characters. It shows they're involved. They care. They play the character with more "character" because they do, indeed, care if the character succeeds or fails.
The other edge of the sword is that the player who cares a great deal can sometimes be argumentative because he's so protective of his character.
That's a hard line to enforce, sometimes, I think as a DM. I want my players to be extremely involved in the game. But, I also don't want arguments and moments that drag the game and make it unpleasant.
The ultimate player, in my book, is one that roleplays, no matter his stats "good" or "bad" (opinionated terms), deeply cares about his character, but also realizes that the game needs an ultimate authority (the GM) in order for the game to flow and that arguments hurt everybody's experience.