Because miners run in pools (typically), the pool (something like Stratum) will create a candidate block and distribute the block header to each miner in the pool for them to work on. In this scenario, miners don't actually have much say over which block they work on.

Miners typically don't even download the full block of transactions as it takes up more memory than required and therefore lessens performance.

That being said, Stratum V2 does allow miners to create their own blocks (as with other miners who use BIP22 getblocktemplate)