That's an excellent question, Mark. But as it pertains to osTicket's core functionality, I think you're more likely to get a good answer if you ask in osTicket's forum.

(osTicket Awesome includes a mod that allows ticket priorities to the changed from the Open Tickets list, but the priorities functionality itself is a part of osTicket's code).

Upon further reflection, I came to realize that I've always been able to set a priority when I'm opening a ticket.

You have to set it up manually, which can be done here:

Admin panel > Manage > Forms > Ticket Details