This is very rare these days isn't it? Who was the last player to do it?
If they had in a transfer request they lose their loyalty bonus, which can be to the tune of many millions. And it doesn't guarantee you a move at all, so you've risked losing a hell of a lot of money for no real tangible gain.
Not sure if it's rare or not. But in the past it seems to me like a lot of moved happened swiftly after a player handed in a transfer request. The likes of Suarez and Coutinho spring to mind.