The working poor pay into FICA which is a greater percentage of their cash flow. They get it back upon annual tax reconciliation. The same entitlement programs nonetheless have lots of unfunded liabilities so the money has already been allocated even if it's not currently "there" -- 'The Rich' are beneficiaries of entitlement spending too.
It's a simpler situation than that. Regardless of proportions of payment, we already have a percentage of the population whose public services are paid for by someone else, either directly through income or divided tax or indirectly through higher prices from corporation tax, or more indirectly through inflationary monetary policy.
In other words: we don't need to invent taxing people with more money more. We have that. Millions of people are partly or fully paid for by others. We might want to adjust it, but we don't need to pretend we're doing something revolutionary in doing so.
This already happens. Many people either don't pay tax, or pay less tax than they cost.
> The government doesn't need to handle capitol allocation.
Then who will spend the tax money?