I remember scorching days in the Lake District where the water in some of the tarns was FREEZING cold.
At one, a group of us were proposing to jump off a dam wall into deep water. I think our OBMS instructer had warned of the dangers of the water being cold and fortunately I thought to test the temperature. I waded in from the side, I might have gown icicles on my 1% 0.25%, it was that cold.
I stopped the jump.
I have often wondered if I stopped heart stoppages that day, the shock of jumping from the heat into the icy water would have been at least breath taking.
I remember another time, years later, where swimming breast stroke or crawl my shoulders started to lock up and I would say I was a strongish swimmer at that time. I had to roll over on to my back and complete the trip to shore on my back,
I've never really tried river swimming but if they can be equally as cold I think it would be inadvisable to quickly swim or jump into deep water, plus I'd bet most of the time you don't know what junk lies below the surface.
I also wonder how many people in trouble in deep water in a river, especially kids, would try to make it back to their friends or entry point. I've seen dogs do that and walked down stream calling to them so that they didn't have to flight the current. A la, instead of swimming to the side of a rip tide people in difficulty often try to swim to shore i.e. up stream = thank you Bondi Rescue on you tube.