There's an additional factor at play, which I don't think has been mentioned yet.
I live at sea level, and I can't even think about doing Whitney without spending at least 3 or 4 days acclimating. So no matter how same day permits are issued, it's really not ever going to be a practical solution for me. Aside and apart from making travel plans to come from the east coast, I need lead time that same day permits don't offer.