Legitimate sportsbooks with casinos tend to pay very quickly. The majority of casinos I've played at tied to a sportsbook with a B or higher rating at sportsbookreview.com have paid in a matter of hours, not days. And none, with the exception of Mansion, have requested ID when I've used Neteller.
I've received same day first time payouts from all of the following
Bodog (RTG)
VIP (RTG)
Mansion (proprietary)
Canbet (RTG)
5dimes (Unified?)
Pinnacle (Blue Chip)
Carib
Bet365 (playtech)
WSEX
BetWWTS (Playtech - BetCasino)
Dimeplayer
Unless it's for bonus whoring, I have no idea why someone would play at a Playtech that waits 4 days to process payouts, when BetCasino and Bet365 are available. Same for RTG when Canbet, Bodog and VIP are around. Unfortunately, the only microgaming sportsbook-affiliated casino I'm aware of is Intertops, and their payments have slowed dramatically.