Which I'm actually OK with: I would be perfectly happy to trade UBI for no minimum wage, from a human-welfare point of view. Right now, people choose to work for wages below the cost of living because starving to death slow is better than starving to death fast. With UBI, the "don't accept/stay at low-paying job X" penalty is just a loss of marginal income, not an existential threat. Some people will work for peanuts because the job isn't that hard and the extra marginal income is nice. Other people will feel more empowered to tell employers offering shit pay for terrible, unsafe work to shove it. So you'll get wins on both sides.
(On the other hand, the government may need to mandate minimum wages just to ensure there is enough of a tax base to continue funding UBI, which is a different issue.)
I think UBI is different in that everyone is given a certain amount of money as a basic human right, and then people can be paid market rate for the work they do.
You're right about the security that UBI offers though, and I think that removing the minimum wage would go well with introducing UBI. In some developed countries without a minimum wage, unions set the pay rate for specific jobs, a similar arrangement happens in Australia, where people are paid according to industry agreements on the value of a worker.
Which I'm actually OK with: I would be perfectly happy to trade UBI for no minimum wage, from a human-welfare point of view. Right now, people choose to work for wages below the cost of living because starving to death slow is better than starving to death fast. With UBI, the "don't accept/stay at low-paying job X" penalty is just a loss of marginal income, not an existential threat. Some people will work for peanuts because the job isn't that hard and the extra marginal income is nice. Other people will feel more empowered to tell employers offering shit pay for terrible, unsafe work to shove it. So you'll get wins on both sides.
(On the other hand, the government may need to mandate minimum wages just to ensure there is enough of a tax base to continue funding UBI, which is a different issue.)