I don't think it's always the case that the market will eat any attempted improvements - it's just that an attempt to raise the wage floor without any other changes isn't enough to prevent the market from adjusting to the new baseline.

There are tons of other ways to change the calculus. E.g. tax code, employment laws, separating health care from employment, etc. I'm no expert and I don't know what the 'right' answer is but I imagine it's some combination of thought-out policy changes that, when combined, apply an economic force to pull the wealth gap closer over time.