If you use these questions in your interviews, you are selecting for skilled liars.

If that job starts with a demeaning exercise, how many more of them are ahead?

Testing for desperation is an abuser behavior. They're looking for ability to control, ability to get away with things. I strongly encourage people to stay far away from companies that hire like that.

Won’t that select for desperate candidates that don’t have many options? Wouldn’t a company prefer candidates that are so desired they don’t feel the need to do do the limbo?

On the face, maybe, but if they qualify and they're desperate, they'll agree to a lower salary and be less likely to seek out a competitor to work at.

In contrast, someone who doesn't feel pressured to take this job or else will seek a more competitive pay, and maybe leave for another job if they're dissatisfied.

The desperate candidate that you underpay will lose the desperation after getting the job, realize they are getting ripped off, and leave much quicker than someone compensated at the market rate.