It is not hard at all to fight a fish from a pontoon boat, I have done it on lakes and ponds many times. I don't think that is the appropriate concern. Much more important is the flow of the river, your method of propulsion (you need oars), and whether you can keep your feet out of the water.
I have floated the Saugeen River in Ontario in my 'toon, it has a moderate current. I went over some riffles and through deep pools with no problem. Over the riffles I made sure my feet were up on the footbars and did not catch on any rocks to flip me. I abandoned my flippers almost immediately as they were insufficient in controlling my drift. I used the oars to face downstream like a drift boat and control my direction. One of the main problems was drifting though the good pools too quickly and having trouble rowing back upstream to drift down again. My friend in a kayak had a better time, but he also had to paddle back upstream several times to get a second drift. Neither of us had anchors. We found it better to park the craft at good pools to wade and cast. At the end of the day I had to paddle quite a way downstream through slow current to the take-out. 'Toons don't move fast and it was quite tiring (and boring). You will need to know the water and know your route quite well and I think this is much more relevant than the technical challenges of catching or fighting fish from a 'toon.