Minimum wages are not "good on their own"; they're a solution to a specific problem: making sure people can survive with at most a relatively reasonable amount of work, though they're currently failing at that goal. If we stop having that problem we stop needing a solution to it. Making it so people don't need to work to survive is strictly better.
And if people have a guaranteed level of support, then yes, there is a downside to saying "you're not allowed to exchange sub-self-supporting amounts of work for money". You don't need to ban wasting people's time; if people don't have to work to live, the uninteresting or unpleasant jobs will be having to raise pay to get people to work them, or figuring out how to automate them when previously it was cheaper to pay minimum wage.
Meanwhile, there are plenty of things people might want to do that aren't valued enough by society to pay even subsistence wages for. In a minimum wage world, those things either don't happen or they happen as side hobbies for people with other means of support. If you have UBI, you create the perverse situation of "I might do that for free because I don't have to work to live, but I can't take any money for it unless I can get someone to give me a lot of money for it".
> the uninteresting or unpleasant jobs will be having to raise pay to get people to work them
They do /eventually/, but because working takes time, working a bad job reduces the time you have available to find a better one, which has the effect of giving everyone less than ideal work situations. That's why it's called search theory.
With UBI, people don't have to worry as much about lining up the certainty of a better job before quitting a worse one, and people aren't likely to take those worse jobs in the first place unless offered substantially higher pay than they'd have settled for if they needed the job. That and other factors seem likely to make search theory around the minimum wage boundary much less of a problem with UBI.
And if people have a guaranteed level of support, then yes, there is a downside to saying "you're not allowed to exchange sub-self-supporting amounts of work for money". You don't need to ban wasting people's time; if people don't have to work to live, the uninteresting or unpleasant jobs will be having to raise pay to get people to work them, or figuring out how to automate them when previously it was cheaper to pay minimum wage.
Meanwhile, there are plenty of things people might want to do that aren't valued enough by society to pay even subsistence wages for. In a minimum wage world, those things either don't happen or they happen as side hobbies for people with other means of support. If you have UBI, you create the perverse situation of "I might do that for free because I don't have to work to live, but I can't take any money for it unless I can get someone to give me a lot of money for it".