Once I started up a PbP 3.5 game on RPOL (is it .net or .org? Don't remember.) Most of the players were friends, but I left it open to others.
One guy, one of the others, wanted to play. He was enthusiastic. I said OK.
He wanted to play a Druid. Fine. We were starting at 1st level. He came back to me with a whole huge back story.
His PC was the son of a High Druid Priest, who was also a merchant in a caravan, and he had wandered all over the world and seen all sorts of sights in his wanderings. Now he was coming home to take his place as a druid initiate, and loot tombs for gold, as druid initiates are wont to do.
I could see what he was doing. It was blatant. He didn't want to get called out if he tried to wild shape into a python, or an emu, or an unladen African swallow, or whatever. He wanted to be able to say, "sure, I saw one when I was traveling in the caravan." No way was I, as DM, gonna screw him over on that! So he thought.
Then he gives me his goals for the character, vaguely disguised as his 'take' on who this guy was. He was a natural shapeshifter, more than a spellcaster. He was in tune with nature, and animals and stuff. And because of this, he naturally wanted to take the 'natural spell' feat, which was one of the few I'd said at the start I didn't like and wasn't going to allow.
For those of you not well versed in 3E, Druids don't get Wild Shape (ability to change into animal forms) until 5th level.
And I repeat, this was a PbP game (S......L.......O......W......!), and we were starting at 1st level.
More recently, in my long prepared but short lived Maritime Campaign, Alex, at character creation, wouldn't be satisfied with the starting options I'd given him. He wanted more. And more, and more. He wasn't satisfied with a +2 sword for his 5th level Fighter. He thought it was lame. Maybe I should have given him a max. Int, max. Ego intelligent sword with a bevy of awesome powers (detect minerals!), and just had it control his PC at the first opportunity. But I'm not that much of a dick. Anyway, then he wasn't satisfied with the small sailing ship they were getting for free. He wanted a large sailing ship, or a warship, or preferably a large warship.
Getting that sort of stuff from the beginning, I wondered, what's left to adventure for?
Now, I've had my share of characters who I came up with the concept first, rolled later. Or even a few where I've been asked for, and provided, a few pages of back story.
But I don't have many interesting stories about those characters. Not the way I do about Belrain, the Chaotic Elf with a penchant for fireballs (especially from wands, or his Staff of Power), or Skarp-Hedin, the Dwarf Fighter-Thief who ended up on the wrong end of too many monster beatings but always managed to pull through.
Long story short, I find that exploring characters is more fun, and more memorable, if it happens in the game. Doing all that work before hand, then having to hog the limelight during the game to get all that exposition across to the players? Not so much. Not being satisfied with the starting conditions of the game, because it doesn't match the idea I've got in my head of who I want this PC to become? Definitely not.
I find it similar to the way I don't enjoy 'tournament Magic: The Gathering.' I always found the game the most fun when waiting to see what I'd pull out this round, what my opponent would do, and the randomness of it. Having a carefully constructed precision deck where I've got a plan of how I can beat anyone in 8 turns or less? Boring!
I enjoy the action and response, the way my character interacts with the other players' PCs, with the DM's world, and with the results of the dice. In other words, not knowing exactly who this character is--maybe I've got a few ideas, but nothing is certain--does it for me. Besides, the whole point of 'character exploration' is seeing how that character will change and grow.
If you've already 'grown' that character before play starts, what is there left to explore?
Your mileage may vary.