Personality is important! It's important in the part of the game that, earlier on, had no rules to it. The only "personality" the game demands is to play to one's alignment. Even Charisma is not so much personality as it is a mechanical stat that helps adjudicate how persuasive your figure can be,
As the import of "role-playing" as we know it today increased (and as the concept of "player" and the concept of "character" became distinct from one another), more rules were added to reward playing a role at the table.
But in the beginning, role-playing was its own reward. And that is a good thing, because not everyone likes to do it or is clever at it. But Dave Arneson invented the Platonic idea of the role-player as it pertains to D&D back in Dave Wesley's Braunstein games.
In my version of D&D that I wrote, there are no rules for RP other than Alignment (which dictates languages and the Cleric's conduct). There is still a ton of RP that goes on - there's just no in-game reward for it; I have found that the table reward is enough.
It's difficult to become attached to a particular chess piece in a particular game. That's because the pieces have no personality and we don't expect to animate them with our own. They're just machines. In the same way, a PC with no personality is a machine. He's just not going to be as much fun, nor will you become attached to him.
It is through the special alchemy of RP that we are able to turn paper men real in our minds and therefore fall in love with them and with the game as a whole.