When you're flying first class, you shouldn't have to wait. The whole point of priority check-in is to beat the queues. Standing in a steadily building queue for ten minutes is just not acceptable when you've paid/used your hard earned miles to travel in First.

Luckily, an efficient and friendly customer service agent stepped in after ten minutes to deal with us, or it would have been a lot longer. Perhaps it would have been quicker to use Slow Bag Drop, but you shouldn't have to down-grade yourself when you're flying F.