Let's end this discussion once and for all.
Do bookmakers have to offer you a service?
No they don't.
Should bookmakers be allowed to have discretion when choosing who to offer a service to?
Well, that's debatable. I wish the answer was no, but unfortunately it's probably "yes".
You're point is obviously correct but it's a murky area because when you join there is nowhere that states that "hey if you win we will ban you and if you lose then you'll be our best friend". I don't think that the average punter would have the knowledge that bookmakers would ban you for winning - especially since some of them run with slogans like "take us on".