Traditionally, after the first autumn spates has cleaned a lot out, weed is also less of an issue on a river. In general fish may also be feeding well to build up reserves for the coming winter. Septemebr is a good month because the leaf fall hasnt started - once you get windy spells in late October/early November and leaf fall is in full swing it can be a pain o the river whether float fishing or ledgering.
The shoaling up in deep water happens in mid-winter. If you can find where the shoals go (if the cormorants havent first) or you can find a warming influence that attracts them, then bumper roach bags can be the reward (or were, once upon a time).
The pike season used to start in earnest on October 1st and still does in some venues. Dont know why winter is productive for them - not a pike angler, but they are at their largest in about February prior to spawning.
Presumably floods also wash some of the smaller fish away , but not in lakes , I remember fishing a commie a while ago , carp only pool and getting millions of bites from very small carp maybe only a couple of inches long, baliff said most would be lost over the winter , I wonder to what ? Though terns , i think they were seemed very active.
Do lake fish go into some kind of dormancy over the winter ? Especially when the ice starts to form, hence winter fishing on commies can be all about casting around with small / single baits and trying to drop it on a carps head.
Canal by me has gone very clear , about a month ago I was amazed to see two jacks next to each other with hundreds of very small fish swimming around them. , right near their jaws , so in answer to the OPS question it all depends where you are fishing.