What actually happens is that profit margins get hammered (notice how you forgot about those? they can go down too) and those businesses that rely upon minimum waged labor complain bitterly.
Very low margin businesses do raise prices but in the studies I saw the only two examples from a wide survey were, like, nail salons and catering.
The whinging manifests as money piled into lobbying and public outreach to prevent this type of thing from happening again and the result of that public outreach is where you formulated your opinion about what happens.
So I live in a country with no rent controls with very high rents and housing costs. The capital is disincentivized from creating more supply by the fact that creating more supply devalues existing supply.
Rent controls would 1. lower the rent (obviously), 2. lower the price of existing apartments since the profit you make on them is lower, 3. like a sibling comment points out, hammer the profits of capital.
> Taxing the rich lowers the velocity of money, disincentivizes capital to search for more profit seeking enterprises.
Wow... Taxing the rich means less taxes for the poor means more people with money/time to start their own companies.