I think that guaranteed income shouldn't replace minimum wage. The reason is that when workers are willing to work for $1 an hour "for the experience", you're basically just subsidizing companies that don't pay a living wage to their employees. If you want to be a volunteer, or you want to be a startup founder and be compensated in equity, that's fine. I'm just not okay with the idea of shifting the cost of employing workers in dead-end, menial jobs onto the government.
With a (sufficiently high) guaranteed income, there is no such thing as a "living wage." A "living wage" is $0. And it goes to everyone, so it's not as though the government is in fact "subsidizing" any business -- they pay the same amount of guaranteed income whether the minimum wage is $0 or $100, whether people are employed or unemployed.
A guaranteed income should absolutely reduce the minimum wage. That's one of its major benefits: redistributing wealth without distorting the market. And I wouldn't worry about the idea that any rich people (the people who presumably you're ultimately worried about subsidizing when you use the shorthand "subsidizing companies") are going to be unfairly benefited by this scheme: it's pretty massive wealth redistribution from the wealthy to everyone else.