I disagree with the proposed solutions, all way to complex. The thing to do is simply give the subsidy to everyone and make up for it with higher taxes. That is

I disagree with the proposed solutions, all way to complex. The thing to do is simply give the subsidy to everyone and make up for it with higher taxes. That is how you achieve more equable outcomes, give fixed subsidies to everyone and recover via proportional taxes. Instead we end up with a situation where we have arbitrary cutoffs, a large buerocracy just checking for eligibility and often even progressive subsidies (giving more to those with higher incomes)