Yes, a company is a group of people organized with a central purpose. However, companies are not allowed to coordinate with each other to fix pricing or availability or other terms. Nor are they allowed to take actions that shut non-coordinating companies out of the market. I may be wrong, but it is my understanding that unions do not have these constraints and, in fact, the reason they are even legal is due to statutory exemptions from anti-trust law that makes that combination of "purpose" an option. So to me, it's not an apple to apple comparison. And that's the problem of principle that I have. I don't think a market operates well when the ability to fix it is granted to some parts but not others.
The comparison to me would be operating only within a single company. I don't think there's anything stopping a group of employees from using whatever bargaining value they have to move the company in one direction or another - whether it's pay, working conditions, product development, etc.
What you say about unions having fewer constraints is interesting. I think it's important that both sides be made to play fair in such things, and the laws could use a review. I just think in principle unions are important in certain industries due to the structure of the industries themselves. Especially ones with a centralized nature, such as trains, electricity, cable TV, and fossil fuels. That unions are important in these areas is shown by them having a longer, stronger history of such.
The comparison to me would be operating only within a single company. I don't think there's anything stopping a group of employees from using whatever bargaining value they have to move the company in one direction or another - whether it's pay, working conditions, product development, etc.