> no need to tax them more to solve THAT one, just make them pay a living wage.
Thereby reducing the scope of jobs for which they can hire to ones that return sufficient value for that, sure.
Of course, that will add to the public welfare burden, not reduce it, since it will reduce employment.
There's a very good argument for some minimum wage in the absence of better of minimum support policies like UBI (that is, while it may not be the ideal minimum support mechanism, there's plenty of evidencie that, to a point, minimum wage is a net gain compared to not having it.)
There's also probable a decent argument for “living wage” (sufficient for independent support) as a floor for certain kinds of labor in government contracting, etc.
There's not really a good argument for living wage as the minimum wage floor; making everyone whose most valuable labor is not sufficient valuable to support them independently unemployable rather than employable at a level from which they can gain experience and advance is good for neither the unskilled nor the broader society.
> to solve THAT one, just make them pay a living wage. Nobody working full time should be below the poverty line, nobody working half-time should require food stamps - otherwise it is exploitation not employment.
This argument is equivalent to: “No one whose full time labor returns less value to the employer than would merit pay above the poverty line should be employed at all; nor should anyone whose half-time pay would leave them eligible for food stamps.”
Making the relatively unskilled completely unemployable isn't helping anyone. (Also, food stamp eligibility limit is generally 130% of the poverty line, so aside from the general outline being bad, the specific details you've chosen would set a minimum hourly wage for half-time work at 2.6× the minimum for full-time work.)
It's much better to tax capital income and increase the minimum support floor independent of employment than place increasing demands on employers, which just promotes automation and reduction in employment. You want to improve conditions for workers, especially at the low end? Tax capital income equal to labor income—both the basic income tax and the payroll/self-employment tax employed to labor income (this also includes uncapping the social security portion of payroll taxes.) Use the added income tax equivalent revenue to fund broad, unconditional minimum support (it won't be anywhere close to a mature UBI initially, but that's okay.) Use the added payroll tax equivalent revenue to (1) provide SS and Medicare eligiblity based on qualifying income that isn't labor based, but with (for SS) additional high income “bend points” beyond those in the current formula so that the marginal additional benefit for additional income continues to drop with income, (2) provide additional security for payroll tax funded programs, (3) beyond what is actuarially needed for long-term program security, transfer the excess to fund additional broad, unconditional minimum support. After indexing minimum wages to inflation, reduce the by $0.01/hr for every $40/yr of the minimum unconditional support (that is, full-time minimum wage would be reduced by half the unconditional benefit.)
Workers are, in net, better off. Those unable to find work are better off because of the unconditional benefit. Taxes paid are fair, income is income. There's less incentive to reduce employment, and indeed more people can be employed.