The network does not elect a leader. that is a mischaracterization of the PoW process. It's not like you are hashing based on your public key or something and

The network does not elect a leader. that is a mischaracterization of the PoW process. It's not like you are hashing based on your public key or something and then you get to sign a block afterwards. You have to commit to a block template before every hash. And also the miner is decided randomly by a weighted hashrate. Imagine applying this to anything else. The group with the most (extremely specialized) computer power just gets to decide everything?