I think you're underestimating how important that flexibility is to a large contingent of people. I have talked a lot of Uber/Lyft drivers and have heard a ton of stories about how valuable that flexibility is. It's huge for students who are in school, for people who already work another job but want supplemental income, people who are mostly retired (or never worked) but have some new expense come up (one lady I spoke to recently started driving for Uber just to help pay for her daughter's upcoming wedding), people who are pursuing careers in music or other artistic endeavors, entrepreneurs who need a way to pay the rent while getting their business bootstrapped, etc.
For a lot of people in those situations, the control over their time really is a crucial aspect of what makes Uber/Lyft desirable.
Granted, that's just one aspect of the gig economy, but it seems to be a big one.
Strongly disagree. Waiting tables or bartending at high-end restaurants could be considered gig work. Wedding photography is gig work. I have a friend who runs a stationary side business as a "gig". These jobs, if you are able to market yourself effectively and gain a good reputation and some solid contacts, can pay extremely well. I have a nice 9-5 with benefits and stability, but my friends in the above positions earn about the same I do and work close to half of my hours.
That obviously isn't the case for everyone who does these, but I don't think you can make the claim "the pay sux" for all gig work.