Suppose that Bitcoin nodes had no target difficulty at all, and instead just accepted the block with the largest PoW every 10 minutes. Ignoring the increased bandwidth (since nodes would be broadcasting several block candidates), would this work? Or is there some technical need for an adjustable target difficulty?
Edit: to clarify, I meant that every block is accepted, but only the chain with the largest accumulated work is considered canonical. I.e., if there is a weak block days ago, and you mine a block with higher score, that weak block does not become invalid. You need to replace every block on top of it if you want to rewrite the story that far. I.e., it is the same as Bitcoin, without a target difficulty. Nodes just accept all blocks, and compute the best block by summing the accumulated work of each candidate tip.