There's no reasonable way to leave it in the river without it getting destroyed by ice. The ice freezes to the bottom and the silt bottom constantly shifts. Even if there was a way to anchor it to the bottom in deep enough water (that wasn't a mile away), everything would be destroyed during breakup when the multi-ton blocks of ice and whole trees come crashing through.
This are has a long history of fish wheels for catching massive amounts of salmon, so the concept isn't entirely untested. Other than the ice, this river has a significant amount of drift from the size of small sticks to whole spruce trees floating down in the summer. One of the primary tasks of running a fish wheel is removing the jammed drift and repairing the damage it does as it's getting jammed then jostled by the current. I suspect there is some cultural wisdom in the total absence of wheels generating electricity here.
I've considered building a fish wheel that also has an integrated generator. But at this point, we can't handle that many fish.
None of that is to say "it can't be done", it's just that an efficient charge controller is way higher on the simplicity scale.