If you play with bitcoin you don't have to verify any details or share any personnel information. Once you nominate that the currency of choice is bitcoin then the form will remove sections that are not needed. So players do have complete anonymity.
If indeed you set that way, I quite agree with you make it so that people who want to play on your site will be very easy and convenient. The rules may have to wait to get into the gambling sites you will be very safe for this sort of thing.