This has been my experience in nearly every game I've run or played.
DM: "I'm running a game with X, Y, and Z characteristics"
Player: "Cool. I'm in. I'll go make a character that fits!"
And again, experiences differ. I've done that, but found it to be a much more rewarding experience when I say:
Me (DM): "OK, I'll willing to run the game -- what characteristics do you guys want? I'm thinking X, but can you give me Y and Z?"
Player 1: "Cool! X is great! And for Y, I'd like some swashbuckle-y stuff!"
Player 2: "And maybe pirates for Z, and they also fit Y!"
Plater 3: "Swashbuckling adventures works for me!"
Player 4: "Just tell me what kind of character will fit, and I'll make that."
If everyone was like Player 4, I'd quit DMing.
As a GM, I'm not great at improv. Espectially world building or large scale plot improv. Things take time to gel. If I had that conversation and hadn't already been thinking swashbuckly pirates, I'd probably reply: "Alright, give me a month or two and I'll see what I can come up with." By which time they'd probably be excited about something else.