You'd have to assume any of the players gambling on football would also be gambling on other sports. I don't think banning them helps, and it also doesn't address the issue.
My personal opinion is it's just a compulsion to gamble and isn't specific just to one sport. Also, how does a Newcastle player betting on, say, league two and German football even become an issue? Betting on the any competition they are directly involved in could be a conflict agreed..