Employers don't pay $5 per hour because they wouldn't make a profit either.
In my own experience I've had several prospective employers at conferences say that they were interested in poaching me but mentioned that they were wary to start a poaching war. They knew the CEO of my company and were conscious of the fact that he would likely make an effort to respond in kind. The Nash Equilibrium is an interesting concept but reality is complex and messy.
[1] https://equitablegrowth.org/aftermath-wage-collusion-silicon...
But back to the central point the basic nash equilibrium is in the spherical cow realm of models as they relate to actual reality. There are some interesting additions to it involving time series and asymmetrical information to try and model real economic data.
Nope, they might be able to make profit at $5 or $10/hr, but there it doesn't make sense to pay more than you have to, that's why Chinese devices are significantly cheaper than their western counterparts, they can still compete if they raise the prices but they can allocate cheap labor in china that allows them to become a strong competitor
Big tech companies, maybe. But even those.
Once you raise prices the demand shrinks which also leads to smaller profits. There's no free lunch. If employers could make more money by paying higher wages, they generally would.