The solvency or insolvency of the so-called Social Security trust fund is irrelvant. The trust fund is an artifact of bookkeeping, not a real asset. So, forget the trust fund and focus on what really matters: taxes paid in and benefits paid out.
Taxes paid into Social Security don't yield real returns. Social Security is merely a transfer-payment Ponzi scheme that's going to begin claiming victims in about 14 years, when benefits begin to outrun taxes.
Private accounts, on the other hand, would yield real returns. Thus, investments in private accounts would provide income that doesn't depend on transfer payments.
The only question, then, is how to make the transition from the present Ponzi scheme to a system of private accunts.