While supply and demand is a good model, it is at the end of day, still just a model. Even as a model, it is not easy to apply to real-life situations. Measuring supply and demand is not easy. Constraints on supply and demand change all the time. Complements and supplements change all the time. Second and third order effects which take a long time to show, but have massive impact cannot be easily predicted and measured. Finally, the supply and demand logic requires a perfect market, which does not exist.

It is great model when you have perfect information. I would like to present the Economics Anti-Textbook - https://www.amazon.com/Economics-Anti-Textbook-Critical-Thin... for a more nuanced approach.

[Edited for missing a word]

This isn't the first such study, in fact there is a long history of them, with results so mixed that nothing can be concluded one way or the other on minimum wage (except perhaps for the conclusion that Economics 101 models don't match the real world). The following book contains a short review in an early chapter https://www.amazon.co.uk/Economics-Anti-Textbook-Critical-Th...

Still to my mind, a high level of Universal Basic Income combined with no minimum wage would be a more logical thing to do, and solves the above problems.