This is 100% true and a demonstration of the dominant power of capital under capitalism.

At the same time, don't forget that even if minimum wage were pegged to inflation, there would still be expropriated surplus labor domestically as well as imperialism internationally. I've seen socialists get sucked into fights over the minimum wage and eventually lose their sense od priorities and messaging until they are indistinguishable from "progressive" liberals in both word and action.