Join Date: Feb 2007
Location: Pensacola, FL (PNS)
Programs: Delta 1.99M, Hyatt Globalist, IHG Diamond, Marriott Gold, Hilton Diamond
Posts: 2,717
Mine (a renewal, so take with a little grain of salt) literally took two days.
Submitted application > processed > new one sent within 2-3 days.
So by that metric, they're either (1) not busy, or (2) have a lot of capacity.