Limited liability isn't for its own sake, it's intended to make the market for investment--the deployment of capital--more efficient.

An employee doesn't actually enjoy limited liability, but he doesn't need it because employees aren't jointly liable except if they directly cause an injury. If a UPS driver runs over a kid, both the driver and UPS are jointly liable, but other drivers wouldn't be liable regardless of limited liability laws. The point of limited liability is to shield passive investor-owners from joint liability. Without limited liability there would never be such a thing as passive investor-owners (e.g. shareholders) because anybody with money to lose would want to have a regular and direct management role to ensure the company didn't do something stupid, like hire inattentive drivers, that would put all of their other assets at stake. All their other assets would be at stake because owners are normally vicariously, jointly liable through the doctrine of respondeat superior. "Limited liability" means liability is limited to the investment.[1]

Similarly, the rules for forming legal business entities in general (whether with limited liability or not) are not for their own sake. The point is to provide a prepackaged set of legal rules that reduce the transactional costs in organizing and running cooperative business ventures. The transactional costs of making constant, 1:1 contracts would often prohibit otherwise socially beneficial economic activity, especially when you consider that business entity rules don't merely complement and substitute 1:1 contracts as between members but also complement and substitute for the contracts and other legal relationships those members make with third parties (e.g. customers).

Abstractly, these are very much the same reasons why you might want to permit unions: collective bargaining overcomes the transactional costs of each employee negotiating 1:1 with the employer-owners. And those transaction costs disfavor employees precisely because the employer-owners already benefit from rules that make it cheaper to organize and manage the business.

Now, maybe there's much more value in optimizing investor cooperation than labor cooperation, and so you could absolutely make an argument for why we should have specialized legal vehicles for investor-owners but not for laborer-employees. But that would have to be an empirical argument to justify the asymmetry, unless for some reason you simply believed wealthy people (those with enough money to be investors) were inherently more worthy than others. You can't simply accuse a union alone of being a cartel, because it's just the flip side of the capitalist/laborer coin.

Note that the antitrust immunity enjoyed by unions is, at least theoretically, constrained to permitting individuals to "conspire" in the market for their labor. But that's no different than what investor-owners are doing in a corporation--"conspiring" in the market for capital in a way that increases the conspirators' profits as compared to if each conspirator had to be an active participant in each venture in which he wanted an ownership stake.

[1] A negligent UPS driver's liability isn't limited to the economic benefit (e.g. wages) derived from the particular economic activity he was engaged in. His $50k inheritance is at risk, too. Limited liability is the exception, not the rule.