What you're missing is the increase in production that comes with the higher employment. That tends to negate inflationary pressures. Right now we have a minimum wage that creates unemployment. Those people don't produce. This unemployment also tends to place additional burdens on the rest of us, like additional crime and funding of social services. All of this things tend to increase prices.
A "matching funds" approach, on the other hand, would take people that were previously unemployed and make them employable. Crime reduction and welfare reduction and increased production would result.
Now the benefits of these things are generally distributed throughout society. This creates a "free rider" problem. It isn't unreasonable to ask that those that benefit from this arrangement to pay for it. Besides, most of the public want to help these "bottom" income earners. A tax for this purpose isn't that unreasonable. It certainly is much better than having a minimum wage.
On the other hand, idiocies like yours would help to further stimulate the underground economy and barter, which is a good thing.
Just the opposite would happen. A "matching funds" approach would bring more of the underground economy into the regular economy since there would be greater incentive to report transactions. This would also have an enormous positive effect on the illegal immigrant issue. That represents a huge part of the underground economy. Matching funds would create huge incentives to bring it into the light. And all this is easily implemented using negative tax rates at the bottom of the scale. Again, this encourages reporting.
I thought that was the democRats' job. We certainly don't need two Big Stupid Government parties.