Those alternatives are indeed all taxpayer funded, but not all act as a subsidy to employers. There was a paper contrasting EITC and guaranteed minimum income, and one of the notable differences is that EITC is a slight subsidy to employers, while GMI is actually the opposite. GMI creates (some) disincentive to work, requiring employers to pay more to attract the same employees.

Conversely, why should employers be the ones responsible for providing a safety net to a nation's citizens?

It's not really a safety net at that point, it's more along the lines of the true cost of the employee. I suppose it all depends on how you look at it :)