if I made a website tomorrow, could I legally run/operate it and accept deposits?
You may operate but attracting deposits would be a big problem. Even in crypto space now a days, people look for registered companies so that they may chase down the owners on the occurrence of sudden shutdown of a business. That must be a good practice for staying/beginning safer.
You cannot think about operating a fiat casino but now in crypto world too people start looking for possible things for ensuring their safer environments.