The entire issue is the connection between welfare, poverty, and the minimum wage; it's all relevant and needs to be accounted for. Lowering the minimum wage would increase the welfare state and poverty, raising it would reduce it. In either case, society pays for it, either through higher prices or higher taxes, but raising the minimum wage would incentivize a working poor vs. a non-working poor; it's obviously more preferable to have a working poor, and it's mathematically proven to reduce the overall societal cost; prices will not rise at the same rate for increase in MW, than taxes increase due to a reduction of MW. Raising the MW is the most profitable option from a Macro-economic perspective, and that should be reflected as stable or even increased profit at a micro-economic perspective. It's all connected.
That's what "inflation adjusted" means; it takes the increase in money supply into account. Without taking that into account, you just have the nominal rate (which also fell to a half of it's peak value during the years I mentioned). It doesn't matter how you want to see the "value" of it, it's value isn't constant and it goes up and down in an irregular fashion.