the idea of sharing work (pooling) is to have multiple workers that work in parallel to each other and not reply on other's solution. each worker gets its own work and submits the result of that work then gets the next parallel job.
if a worker has to wait for other worker to finish then it defeats the purpose and the optimization gained by parallel work.
As an alternative, workers could complete both the first and second processes, periodically send some type of verification they are working. Or a single entity could own many computers, each of which is a miner, and each of which is programmed to send the block reward to the same address controlled by the same entity.
I think you just misunderstood what I said. The difficulty of the first phase is greater than that of the second phase. It means that the difficulty of the first phase is greater than that of the node with the best luck in the second phase, not the node with medium luck.
The first phase of cooperation is not cost-effective. For example, if a miner has a node A, and he adds a new node, when the new node joins in a collaborative manner, their computing power is improved, but luck is not high. When new nodes join in a non-cooperative manner, their luck will increase. If the marginal effect of improved luck is greater than the marginal effect of increased computing power, then non-cooperation is the best choice for miners.
The cooperation in the second phase is meaningless. The work in the second phase needs to wait for all nodes in the first phase to be completed by an algorithm to select the best luck parameters before carrying out the tasks of the second phase. The difficulty of the second phase is very low for the best luck parameter, and the cooperation is meaningless.