I think you are right. Unions are by definition all about a (a kind of external) negotiating power. Such things have no place in ideal and fully efficient free markets where the prices are dictated solely by the demand and the supply.
Either such a market would be robust enough (as in your example) and the union would not be in a longer term viable, or the union would be viable (e.g. some kind of monopoly) thus turning the market into a non-ideal, non-efficient and non-free.
However I am yet to see (or realize that I see) a labor market that would be in any meaningful way close to being efficient and free. The labor markets I see have low liquidity (it is difficult to search and change the work, it takes time to adjust your skills), huge information asymmetry and low transparency, and the most actors are not very "free" (debt, no alternative options...).
People who are laid off don't just quit the union; unions often offer additional support for members who are laid off including aid for job seekers. A great example of how unions exist in a competitive market is SAG-AFTRA which by your own argument simply shouldn't exist. If you're going to make an argument against unionization, you shouldn't take one that can be empirically disproven.
What kind of job seeking assistance are you imagining in a car service union? The services themselves already tell you when work is available automatically and the problem is that there are more workers than there are jobs at the higher wage.
Moreover, if you're going to offer things like that then you have to gatekeep union membership and then your problem isn't that people quit the union, it's that they can't even get into it if they wanted to, and would then happily take any non-union work they can get.
> A great example of how unions exist in a competitive market is SAG-AFTRA which by your own argument simply shouldn't exist.
It shouldn't exist if Hollywood is a competitive market. But it isn't. There are a handful of major studios that make substantially all of the major motion pictures and control the major channels of distribution and promotion.
Before the internet it was effectively impossible to strike out on your own as a high grossing studio. It's still extremely difficult using traditional channels. What we're seeing now is individuals doing it using platforms like YouTube -- but they're hardly making anything like what Hollywood does and the various YouTube celebrities are generally not SAG members either.
This is only true insofar as the market is inefficient.
Suppose you have a free market for car services (i.e. no taxi regulations or similar) and the drivers all get together and unionize. They demand higher wages and get them. The only way the company can pay higher wages is to raise prices, so they do, demand for car service is reduced, and some of those people lose their jobs.
Since they're no longer employed, the people laid off quit the union. Car Service Number Two shows up, has no contract with the first car service's union, pays the original lower wage to the people put out of work, and attracts customers by charging lower prices. That causes Car Service Number One to lose business and have to lay off more drivers who then go to work for Car Service Number Two, and so on until everyone is working for Car Service Number Two. If they then unionize again, Car Service Number Three appears to hire the workers laid off due to the higher wage ad infinitum.
Which is why unions don't work in competitive markets.
> the problem with the free market is that it has to optimize for infinite growth.
There is nothing that requires this. What it needs to optimize for is efficiency. If you're paying $50 then you have to charge >$50 and you lose business to the competitor who pays <$50 and then charges <$50. But at scale this isn't a problem -- when everything you buy costs less, it isn't a problem that you get paid less.
The problem now is regulatory costs and cost disease preventing the lower prices from actually happening in many cases. But you can't fix high regulatory compliance costs by increasing regulatory compliance costs.