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.
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.