At the end of the day, we as a society rightly demand a minimum standard of living for everyone, and we collectively pay for that in one way or the other. Either we pay taxes to fund a welfare state, or we pay inflated prices for goods and services to maintain wage floors. The argument I'm making here is paying taxes for welfare is more progressive, as the burden falls on richer people. Paying inflated prices for goods and services is regressive as it's a burden that falls equally on the rich and the poor.

That is an interesting perspective that I admittedly did not think of.

However why do the prices have to be inflated? Can't the company just accept lower profits? That would be progressive since most of the profits currently go to the rich at least for public companies no?

It would actually be a good thing for the prices to be inflated because that would mean that the market is competitive. In a competitive market, profit margins are typically very thin, so unless the increase in labor cost is passed onto the customer, the business will have to operate at a loss.