Fishing permits are understandable in certain places, like when fees go to directly to maintaining nearby rivers and lakes. They are an important way of supporting the local ecosystem.
But there are globetrotters, thrill seekers, and master anglers who are always after the next Big Bite. I would propose
some kind of fishing licenses, much like one for driving, that states the carrier has proven themselves a responsible angler and has the requisite skills to follow instructions related to the activity.
After passing, it would simply be an annual subscription of sorts, similar to a fancy metal credit card. Wherever you went fishing, as long as you were following local rules, your Angler ID would act as the relevant permit or equivalent. The governing body could call the ID service who would broker a re-reimbursement at a bulk rate.
I also imagine it would become something of a status and cultural icon as well, in the same social bracket as a helicopter license, perhaps, yet also serving as officially recognized identification on par with passports.