“Uber Driver” isn’t a job (in the USA; some other countries disagree); you’re a contractor, and you’re free to find customers via other means (e.g. via Lyft, paying their margins, via word-of-mouth, via your own web site, etc.)
Yes, that may be hard or effectively impossible, but a bad dry wall contractor will not be able to hold his business afloat, either.
Either Uber runs a legal business, in which case I would expect others can start similar businesses, or they don’t, in which case this is like complaining that you can’t start a local mob legally after the one you worked for kicked you out.
Yes, that may be difficult, but Uber has shown it to be possible; ‘just’ find some investor with a few billion to spare, and you can do it, too.
Returning to the original argument: even if Uber drivers were employees, the argument “Uber can’t kick me out because I can’t get a job as an Uber driver elsewhere” doesn’t hold water, and replacing “Uber driver” by “driver” doesn’t change that.
Devil's advocate: Taking the drywall job is akin to clicking the "start driving" button. Once you do either of those things (which you are entirely free to not do on a particular day with no penalty), at that point there is an agreement to try and not skip a wall here and there.
"Dry wall contractor" is a pretty generic job title. "Uber driver" is very specific including the "location" where the driver is working. To make the analogy fair you'd have to do have a "Dry wall contractor for Boeing" or similar.
Unless there are non-competes in place, the analogy is fine. You have the freedom to use the platform or to not use it, and often you have the freedom to use other platforms simultaneously.
Yes, that may be hard or effectively impossible, but a bad dry wall contractor will not be able to hold his business afloat, either.