Manny, it can be done. I fished in many states last time I was out on the road. It was a lot cheaper than just drinking in the hotel bar. While traveling, I would also be looking on line to find swimming pools in the next town as well as jazz clubs and good restaurants. I had many licenses printed out at hotel desks. I travelled with a little Okuma pack rod kit with a few extra spools. I probably fished in at least 20 states in the 12 weeks I was out and most of the time I walked from the hotel or took a cab. The crew, who would be on location before me knew to put me in touch with any local crew guys they picked up that fish. Occasionally I would rent a car (in the Canadian Rockies, you think I'm just going to it around the hotel?) but it's amazing how many towns like Sacramento, Boise, Grand Rapids, and Spokane (to name just a few) have fishable rivers running right through them. I would also just go into a redneck bar and offer to pay for gas, bait and lunch (or if the local producer was cooperating a free pair of tix) to who ever would take me out fishing. A couple of times i rented a rowboat in the High Sierras. And when we were in Corpus Christie with a couple of days off, when I went on a party boat and even had a guide take me out kayaking for trout and redfish, but most of the time I did it myself.
It's also cool to go to tackle shops around the country. Even the big box stores have different stuff. And stuff that doesn't sell in one part of the country works great in another part and so one can get lucky and cash in on a distributor's mistake when they put it on sale for a song in Fort Worth and I pick it up for a song and fish it in NY.
I think a universal license would be prohibitively expensive