blockchain – Could a miner set a maximium transaction fee

Yes, miners can choose exactly what transactions to include in their candidate blocks, including the choice to not include anything at all.

Of course, if a high fee paying transaction is available, and one miner chooses to not include it, other miners still can. This is only untrue if an entire cartel with sufficient hashrate that is actively performing a 51% attack chooses not to include a transaction – in that case, it can be censored as long as the attack lasts.