Well, if they're here anyway, and figuring out a way to work and live here, the local and state government needs to figure out how to deal with that. Do you simply choose to not interact with them at all? Some governments think it's better to acknowledge they're here and at least make sure they pass the driving test and can be insured and not worry about their status. This sounds like it's what Minnesota is doing. We can debate whether or not that's the correct approach.
But when Florida says "drivers licenses from these states are no longer valid IF they're here illegally", we have to ask how Florida cops can tell when they pull someone over? Their algorithm probably has two inputs: "License from Minnesota" and "Looks foreign". There is no way to enforce this without discriminating against people who look foreign. Do you normally take your passport with you on a domestic trip? It sounds like some out-of-state drivers in Florida will need that, otherwise their license will be presumed to be invalid if they don't "look right".