Actually, if I were responsible for investing the nation's retirement fund, I would NOT invest it in the nation's checkbook. That's like an employer taking the employee's pension fund and investing it entirely in the employer's common stock.
Diversify, Diversify, Diversify...
I spoke with a long time former Trustee of Social Security about the SSTF. He said if it were up to him, he would eliminate it and make SS a line item in the budget. It would force legislators to deal with the actual costs of the program present and future and provide more transparency and understanding for the public. The reality is that SS and Medicare are pay as you go programs. All the Trust Funds represent are the full faith and credit of the USG to pay the benefits.
FYI: The SSTF and other trust funds are included in the $14.3 trillion national debt as "Intragovernmental Holdings." It amounts to $4.6 trillion.