And not only fees, but so would Bitcoin security in the form of hashing power.

Just think about it, why would a miner shoot himself in the foot and reject transactions below a certain fee? While he is left with no fees, other miners take what's available and maintain at least some sort of a profit (I'm talking once the subsidy is gone..). It's the same argument for why a market strictly regulated by consumption i.e. a free market would never support a racist business. While the racist business discriminates against the customers, another business opens up down the road who doesn't and simply outcompetes it.

The only way miners could set a minimum transaction fee with an unlimited block size is if it was just one miner or if they form a cartel and somehow are able to prevent any other miners to enter the scene and compete with them.