It comes down to profit. Costs (like labor wages) cut into profits. Capitalism could hypothetically support a high thriving-wage for all workers and still create profit for the owners, but historically the owner intentionally depresses wages so that the owner's profit portion is larger.
High unemployment creates conditions favorable for the owners. It creates leverage for the owners to coerce the workers into accepting lower wages. A scenario where the state offered full employment as a competitive labor market to the private sector would force the private owners to raise their wages. Then they would have to deal with how they want to approach their profit situation. They'd probably just raise prices of their products. But in the end, the owner is making the decision on what the prices would be. Not the employees.
The way it does this isn't by paying workers more than competitors do for the same work. It's by charging customers less than competitors do, which actually selfishly benefits them by increasing their market share, but also distributes more wealth to workers because you can buy more for the same dollar (or the same amount of stuff and add to your savings or pay down debt).
What prevents this is uncompetitive markets, which are occasionally found as a result of natural monopolies, and more commonly found as a result of regulatory capture.
High unemployment creates conditions favorable for the owners. It creates leverage for the owners to coerce the workers into accepting lower wages. A scenario where the state offered full employment as a competitive labor market to the private sector would force the private owners to raise their wages. Then they would have to deal with how they want to approach their profit situation. They'd probably just raise prices of their products. But in the end, the owner is making the decision on what the prices would be. Not the employees.