Real supply and demand will stay the same, real economic production will probably stay the same too. So what's the point? 2000$ only feels a lot right now because it's an amount of money that represents a lot of work for a lot of people. Sure, you can link some small scale UBI experiments, but they have all been done in the context of a broader economy where the amounts given still had purchasing power.
There's a reason why most economists don't agree with UBI. I know people on HN love to discredit economists, but the push for UBI here is ridiculous. It is akin to simply denying a whole scientific field because you feel it's are wrong
Economics isn't a science.
Wages aren't defined based on what is fair or unfair. They're decided based on supply and demand for labor, thankfully.
A "shit job" is by definition one that creates little value because value is defined as what is lost when someone exits the picture. Workers in those "shit jobs" can be immediately replaced so no value is really lost by their exit, so their value is close to zero.
There are two people involved in the transaction: the worker and the employer. The employer will value the work at a value greater than the wage, otherwise they would be more profitable just by firing the worker. Similarly the worker will value the wage more than the job, because otherwise they would quit.
When most people talk about the "value" of a job, they tend to not use either local definition, but from a more global definition of "how bad off would society be if nobody did this job" and that more closely aligns with the employer's value than the worker's (e.g. for services jobs the employer makes money on the spread between what customers will pay and what workers will work for, so clearly customers value the job at some margin above the wage, and we can use customers as a proxy for "society")
Without UBI, the wage is what lets the worker not end up homeless and starving (or begging), so someone with no better job prospects will value the wage very highly. Once you add UBI into the mixture though, maybe it's "move into a larger apartment" or "eat out somewhere nice once in a while" and suddenly they value the wage much less.
If your scenario comes to pass, it just means we've been taking advantage of the people who currently work those jobs because they have no other alternative.