The key phrase here is “regardless of household income.” There’s a very simple way to make sure rich people don’t get free shit, and that’s capping stuff like this so that rich people don’t get to take advantage of it.
I’ll give you an example: there is no universe in which I personally ought to have had my student loans forgiven. My household income tipped into the seven figures during the pandemic. But some debt forgiveness advocates insisted on cancelling “all student debt, no exceptions.” Absolutely not!