Whether leader election happens at the same time as the block is proposed or not is completely irrelevant to the nature of the problem from a distributed systems perspective. The point is that in each round, the leader both wins the election, and proposes the next block. There are other variants of proof of work in which the leader is allowed to continue generating new blocks for a period of time and (AFAIK) these inherit all of Bitcoin's security properties.
Here is my question to you: if the node that wins the election (and the ones that accept its mined block, of course) is not the one voting on which transactions get to go into the chain, rather than be stuck in the mempool somewhere, who is? Do you genuinely think there is no decision being made there?
