Because they were promised it - fundamentally leaving the rich out of the social safety net doesn't even get us much and administrating the distinction costs money, and I am no fan of the wealthiest get additional benefits.
I think solving inequality will not be about reducing access to said safety nets but increasing them for all.
> Because they were promised it
No, they weren't. They were promised a monthly check that, should they become absolutely devoid of marketable skills and liquid assets in their old age, would prevent them from dying in a gutter.
They're nowhere near dying in a gutter.
If you want to solve inequality, stop giving checks to people who spend it on golf trips to retirement villages in Arizona, and give it to people who have 84-month car notes and whose student loans are in forbearance. You only have enough money for one of those two groups, not both, so use utilitarianism to decide who to give it to.
The problem with "solving inequality" is there is no incentive for one to do better. If one can live as well as everyone else, with no effort, why should one make the effort?