They sure could and do if labor is limited. If the supply of labor exceeds the demand, you wouldn't need to undercut; you and your competitor would advertise $5/hr and you would both get a worker. In our current world, we don't see chipotle trying to out compete mcdonalds on wages, so clearly for many classes of worker there is an oversupply of labor.

Sometimes even in the real world things do flip, and there is a demand for low skilled labor that isn't being met. I overheard a few restaurant owners talking about the pandemic and their business while I was in line outside the grocery store a month or two ago. They bemoaned how no one wanted to come back to work at the restaurant since they were making more on unemployment. Neither brought up the idea of paying more if they failed to find labor at that price point in the market. Instead, they quipped back and forth about how lazy their staff are behaving after these owners themselves laid them off not too long ago and put them on unemployment in the first place. This anecdote is American capitalism in a nutshell, imo, just pure cognitive dissonance between the realities of the working class and the perceptions from the capital class.