Because they can afford not to.
You're taking a view of the free market that's a little over-simplified from how it actually works. Most industries have areas where they hit happy mediums, where they don't actually race completely to the bottom. Wages can be a part of that. It requires something to shake up the market to force businesses to start competing and lowering profit margins, which arguably is exactly what's happening right now.
Some businesses are paying employees more, and they're not seeing the same labor shortages. But I think a sizable chunk of businesses are mad about the idea that wages work this way, and their ideology is that the government should make sure that low-income workers always stay in a position where low-wage jobs seem attractive.
A big thing to recognize with economic theory in the real world is that profit margins don't always trend to zero, at least not in the immediate short term. If businesses did all increase their profits to $20 in your scenario, they'd collectively all have the same hiring problems and lower profit margins. So that kind of thing won't happen until an event (a pandemic, increased government aid, better worker mobility, a shift in culture, new companies entering the market) forces businesses to get competitive with each other over a limited resource.
> Maybe the answer is that due to covid (recession, lockdowns), business is down so they can't justify paying each employee $15, because that's close to the value that they provide?
I think that's unlikely, multiple industries (Amazon included) saw profits rise during Covid, not shrink.
And in any case, the market is a big part of determining what value employees provide. If you can't afford to hire employees for $15 an hour, and that's what the market is demanding, then the problem isn't that the employees are overvalued, the problem is that your business isn't sustainable and you can't afford to pay market rates.
That's a big part of how the free market works: there are a ton of business ideas I could pursue if I had access to free labor, but unfortunately in a free market you have to pay market value for things (workers included).
There are lots of ways to think about an economy and market incentives, but surely a pure Capitalist reading of this situation is that if your business can't make money paying market rates for its workers and supplies, then your business doesn't deserve to exist. I'm not sure why I should be sympathetic from any perspective, Capitalist or otherwise, if a business complains that the only way it can afford to operate is if its workers are made to live in poverty and forced under threat of poverty to take low-paying jobs. That doesn't sound like a free market to me.
Higher income ranges are able to save by purchasing physical assets that can later be sold for inflated dollars. But, inflation is damaging to higher income purchasing power as well. There is just more breathing room in higher income ranges. Middle class becomes lower class unless they can manage to earn more.
Inflation is a loss for all but a few. Everybody becomes more poor through inflation with the exception of people closest to the new money. Those closest to new money get to spend it before prices increase.
Wages grow more than prices rise. It would be a better outcome for lower income ranges.