randomly assigned pow? in Bitcoin, every node solves the POW puzzle.

instead, are there cryptocurrencies where a random group of nodes is chosen (before block creation), and only that group solves for the puzzle?
in Bitcoin, every node solves the POW puzzle.


Not really, only miners solve the "PoW puzzle" as you put it, all the other nodes just verify that the "solution" is correct. It is actually random which of the miners solves it, like you suggest, while higher probability of finding a solution is given by more powerful mining hardware, even mining with the smallest computer theoretically has a chance of finding the next block.