I'd be polite, I'd be sympathetic to his reasoning, but under no circumstances will I allow a player to be that kind of a wet blanket in my group. Period.
I see two different lines of conversation here:
1) Should you accommodate the player?
2) Is the player being a nozzle for saying what he prefers?
I am addressing the second, not the first. I don't think there's any problem with telling the player, "Dude, I'm sorry, I don't think this game is for you."
However, I also think that most playstyles are valid, even if I don't like them. The guy isn't a crybaby, or a nutbar, just for really not liking to start a second character in a campaign. And, if he really doesn't like it, it is his *duty* to make that clear before he begins, rather than keep it secret and then have it jump out at the GM if the character does, in fact, die.
Knowing your player's styles ahead of time is important. That requires that they actually tell you, and then you can both make an informed choice, like mature adults.
Here's a question: You've got a player who you think would be good to have in the game, but they may be moving away in six months, or a year. Do you not let them in because they might leave at some unknown time in the future? How is this different from having them maybe leave for some other reason? What reasons are valid for leaving, and what are invalid?