Some hosts don't mind doing this since:
1. You're a new customer and they want your business.
2. If you're paying for Part or fully "Managed" support, so the service is included anyway.
Do you know if you're going from a specific software to software? Such as CPanel to CPanel, those transitions are the easiest. You or your host, should be able to just run a CPanel backup, then import it to the new one.
But if you're transferring across different platforms, then it's more work since it's not as automated.
My current host doesn't use CPanel. I believe they have their own custom interface. I have some time before I make the move as the current host isn't forcing these changes until December, but would like to get things done sooner rather than later if I can.