Unions are anti-free market. They are monopoly cartels protected by the federal government. If people who sell peanut butter joined together to sell their products at a higher price, the DOJ would bust them up. If people who sell labor join together to do the same type of rent seeking, congress sets up the NLRB to protect them.

A company is, last I checked, free to reject the union entirely and fire everyone (if they strike).

Not to mention your argument should be that cartels should be legal, not that unions should not be.

You may want to check again. A company cannot refuse to bargain with the union, and strikers cannot be fired while on strike.

They can however be replaced, in which case the company doesn't need to rehire the striking workers. Potato/potato.

That's not true if the company is in violation of an existing contract though, then the company is breaking the law and must rehire everyone, but I'll reiterate: they're breaking the law to begin with.