Fair, but given that we're talking about a hypothetical government program, "index-based retirement fund" doesn't imply you're the only one contributing to said fund.
This is external to disability insurance that we and our employers also have to contribute to. So I'd agree to a large extent that the govt forcing employees and employers to contribute significant amounts to 401k like programs could be in the interest of everyone in the USA but one needs a disability insurance program on the side as well and that isn't particularly cheap.