In answer to the original question, yes they should. See many cyclists flying down Denmark Hill every morning.
While we are at it, there should be some sort of licence to ride an e-bike (such as Lime bikes) and they should have a number plate and be registered. If they are capable of doing 15mph then they need to be properly regulated.
Again, many people jump on a Lime bike and have absolutely no idea of road rules, which is dangerous for all.