There's no reason why you can't be an employee but also be in control of your own hours. It's not much different from a part-time job that I had while going to school. I'd provide my manager a list of times that I was available to work for the week and he'd slot me into shifts.

Technology has decreased the lead time needed to let someone know that you're available to work to 0. There's absolutely no reason why that should mean that you can't be an employee.