I mostly agree with you but I do think the issue is a lot more complex than that. I do think there is a valid criticism based on market power abuse at the minimum wage in the food sector, for example, especially with the rise of chains over the last several decades and with labor markets at the low end being much more geographically constrained than most analysis of this situation appreciates. In my opinion there is a kernel of truth to the wage should be higher than minimum in many places if the market was functioning properly and had stronger competition but I kind of doubt that's more than a couple dollars and that is being used to push through bad leftist policies to push wages of their special interest groups up when their other policies are highly inflationary in the costs of basic needs like housing as well, which actively harms these people. it would probably help the low end a lot more having policy that generally pushes down the costs of basics (like getting rid of most of the zoning/approvals processes for building anything so people can build whatever fits the economics of the area on whatever land they want in areasonably short period of time, removing carbon taxes, sales taxes on basics, etc).