Personally, I think it's reasonable for a player to want to choose the details of their character.
The DM has the rest of world. The players have their characters.
So, if I came to you and said, "Hey, I'm going to run a game that's set in the bowels of the Free City of Greyhawk. All the characters are going to be members of the largest, most powerful thieves guild. Your PCs will be 1st level, and I'm restricting classes to either fighters (muscle) or thieves. You can play a human, a half-orc, or a halfling. And, I'll give you your character's name once you tell me his race. You'll roll your stats and pick skills and feats as normal.
Normally, I'd let the players pick their character's name, but in this case, the name of the character ties in with prophecy that will become a major part of the story. So, this time out, I chose names instead of letting the players do it.
You'd have a problem with such a game? It doesn't sound like fun?
Characters have backgrounds. Backgrounds are part of the world.
One reason I like to set restrictions on PCs is that I don't like to set restrictions in-game. I love being surprised, seeing what happens. I hate GMing railroads as much as I hate playing them. It's not about my plot, it's about the PCs. That does mean the PCs need to be characters I like and am interested in!
Absolutely. I play the same way. I want my players to have as much freedom of choice in the game as possible.
For example, I'm prepping tonight for our next game on Saturday. The PCs are in a dungeon, and I'm pretty sure that they're going to get out of town while the getting is good and high tail it back to the clan village.
Now, when they come out, they've got three basic ways to go. They can go north, the way they came, but if they do, they know some of the dangers that they will face (considerable), and they saw an enemy patrol go that way just before they entered the dungeon.
They can go west, but this takes them in the exact opposite direction from their clan holme destination and farther into enemy territory.
East is blocked by some steep, unpassible peaks.
And, south leads them into the Cracked Lands--unexplored territory that, on the map, is visually the straightest line back to their village.
As GM, I think the players will go south, and if they do, I've prepared some encounters along the way.
But, the players may, for whatever reason, decide to go one of the other two directions--and although I don't want them to go that way, I will certainly allow it. And, I've set up some encounters to use if they do, in fact, go one of those directions.
It's really up to the PCs to make the best choice for themselves.