No, most low earners are receiving more back in benefits of various types than anything they pay into the system.

Thus if you replace these systems with mandatory investments, you are reducing their available cash.

I think you're either misunderstanding me or how social security works. I'm only talking about replacing social security, not "these systems".

Everyone who gets a paycheck pays their 6% in social security, regardless of income level.

But the curve that determines your payout is dramatically tilted towards low earners: That is, SS pays a much larger fraction of your highest earning years income if that income was low. As a result, low earners have to live only a few years past 65 to receive benefits greater than what they put in. High earners have to live decades.

> Everyone who gets a paycheck pays their 6% in social security, regardless of income level.

Social security tax is 12.4% on the first $113,700 of wages or self-employment income, and 0% on income from all other sources and wages and self-employment income past the first $113,700, so, no, you don't pay "6% in social security, regardless of income level".

(Note that on wages, but not self-employment income for obvious reasons, half of the 12.4% is paid as 'employer share', so that the employee never sees it, so it might appear, if you look only at wage withholding, that the rate is 6% -- or rather, 6.2% -- but that's not accurate.)