Does supporting a higher minimum wage require that unskilled workers are currently getting paid less than their MRP?

If a government mandated minimum wage is justifiable, one thing (I am not saying it would be the only thing) that seems that would need to be true is that unskilled workers are getting paid less than their MRP (marginal revenue product). If their wage is currently equal to their MRP, then surely raising it will result in the loss of jobs. No firm will pay a wage greater than MRP.

So, if workers are getting paid less than their MRP, it would mean that, for example, opening your own fast food restaurant will result in making above normal profit. The new entrants into this industry will increase demand for unskilled workers, raising their wage. So no law would be needed.

Also, if right now McDonalds is making just an average rate of profit, a higher minimum will put them below an average rate of profit. Some would have to go out of business (or not get started in the first place). Again, resulting in job losses.

Maybe the minimum wage proponents would argue that McDonalds is making above normal profit. But then I ask "where are the barriers to entry?" This seems like a very competitive market structure, meaning that there are no barriers.

So competition will drive wages to their MRPs and no minimum wage laws are necessary. If a minimum wage is imposed, it will drive profit below normal or average for some firms. They will go out of business. And some firms will never get started in the first place because the profit would be less than average.