With or without a union, there are no laws I am aware of that prohibit workers cooperating to get higher wages from employers.

That does not violate anti-trust law in the US. It is not a special exemption the union has, it doesn't violate anti-trust law in the US even if there isn't a union involved, for employees to "collude" to get higher wages.

Or if there are such laws I'm not aware of, feel free to share. But I gather you think it ought to be illegal? Why?

Can you elaborate on that? I don't understand what's inherently anti-competitive about labor unions, unless you think that any time humans organize themselves is anti-competitive and the only thing that counts as competitive is a total lack of organization and cooperation above the level of the individual.