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.
^ That is professionally way if you run and operate a gambling site with the complete license to operate. The legitimacy was attracting people to deposit and trust gambling companies if it is fully registered and that should have a license to operate. It would be better if your business is in a legal way and not hiding to your costumers. So, my answer is YES.