[SolarNet]

Tech companies have colluded on the hiring side in the past. But here is the difference. Companies are meant to be entities that provide economic activity through competition (for example on free markets), that's why governments grant them charters that give them tons of rights people don't get (limited liability and special tax rules for example). Unions are designed by workers to protect their rights, originally this was simply through them organizing through their right of free association before the government got involved in it (because they recognize the grant of rights they gave to companies made for an unfair situation in the labor market). Importantly one is something designed to encourage economic activity, and the other is something designed to protect rights.

So no companies should not share the same "rights", because that's called being anti-competitive. Labor unions are only capable of "exert[ing] anti-competitive influence" when unions have recruited every worker (probably for a good reason) or companies engage in union busting against workers who have done nothing wrong (except talk to a union). Don't want to deal with organizing employees? Don't sign a contract with them (the employee-employer relationship also granting companies a bunch of useful rights).