That's not entirely true. Taxes on production and services are ultimately taxes on consumption, this is part of why many economists have advocated for a mix of raising income taxes on specific income brackets and having a more generous EITC.
You could of course do as you propose, but that same logic could also be used to argue that we simply shouldn't let healthcare providers negotiate with employers and instead restrict them to dealing directly with State entities (since otherwise the bargaining power becomes slanted against individuals).
Edit: I didn't clarify well, the reason I mentioned the point about production taxes is because many minimum wage employees work in places like Walmart that sell commonly needed items and thus some of the benefit is lost because you've increased costs for the people you're helping. In theory this isn't a problem for luxury goods but that's more complicated so I haven't talked about those much.
> and thus some of the benefit is lost because you've increased costs for the people you're helping
This is nonsensical. If paying that one dollar in taxes necessitated raising the prices, then the company spending it on insurance would also necessitate raising prices.
You could of course do as you propose, but that same logic could also be used to argue that we simply shouldn't let healthcare providers negotiate with employers and instead restrict them to dealing directly with State entities (since otherwise the bargaining power becomes slanted against individuals).
Edit: I didn't clarify well, the reason I mentioned the point about production taxes is because many minimum wage employees work in places like Walmart that sell commonly needed items and thus some of the benefit is lost because you've increased costs for the people you're helping. In theory this isn't a problem for luxury goods but that's more complicated so I haven't talked about those much.