Don’t think of the minimum wage as a price floor, think of it as a way to create a labor cartel.
If all oil companies get together and agree not to charge more than a certain price for a barrel of oil, they can increase the overall profits of the oil industry at the expense of the rest of society. The danger is that one of them will defect and sell the oil for less, thus forcing a race to the bottom that leaves all the companies worse off. So really what they would like is a way to enforce cooperation, like for example a government enforced minimum price on a barrel of oil.
The situation is precisely the same for workers. We all have labor to sell and would like to get as much for it as possible. If we all compete freely there will be a race to the bottom and wages will be low. If we could all get together and agree that nobody is going to sell their labor for less than a certain amount, we’d all be better off.
The bad thing about this sort of tactic in most situations is that it’s a way of capturing more value for one group at the expense of all other groups – oil companies getting rich at everyone else’s expense. When the category we are talking about is workers though, the situation is different because we are almost all workers or supported by workers. Allowing workers as a whole to seize more value just means that the overall share of income going to workers goes up at the expense of the share going to employers / the people who own those employers.