The basic idea of collective bargaining isn't really illegal when applied to a employers in general, because it's already the norm on that side of the table. A group of businesspeople with mutual economic interest can legally "collude" when they decide what wages to offer employees, how to structure working conditions, how to carry out negotiations, etc., if they agree to form a legal partnership (you don't even need the newer legal fiction of unitary corporate personhood, just a classic partnership structure). Then colluding in business matters is not only legal, but expected. Why can't employees of such a partnership likewise "collude" when bargaining over wages and working conditions, forming into a single joined legal entity that sits opposite the joined legal entity of businesspeople on the other side of the table? It seems much more asymmetrical to say that the group of businesspeople can legally form a partnership to coordinate their economic activities for mutual gain, but the employees must each bargain individually and cannot form a, let's call it "workers' partnership", or union of workers, to likewise coordinate their economic activities for mutual gain.
One thing I find interesting: Will we will see some version of the odd asymmetries between corporate and union law tested out in the courts as the gig economy grows? A company providing labor, for example, can legally ask for exclusivity agreements. Aramark, a big catering contractor, does that frequently. A union can't, though; an exclusivity deal for employees, saying that catering staff can only be hired from a certain union, is banned as a "closed shop" under the Taft-Hartley act. What about a partnership of gig-economy workers? If they're not employees, it seems like they should be able to push for deals more like Aramark ones, even though unions can't do that.