Government is a "pay-as-you-go" system because the real "trust fund" for Social Security is the U.S. economy, and it will draw on it as needed for future bills. Because it can tax, unlike corporate pensions, there is no need for separate funding.
The Social Security trust fund was invented as a fiction to make an increase in payroll taxes politically palatable at a time when higher income taxes were not. The money was never actually intended to be saved for future Social Security. That was just the lie used to sell it.
That said, the only figures that matter are the consolidate deficit ($247B) and debt ($4.8T). The government debt to itself in the "trust funds" could vanish without consequence.
Your explanation doesn't factor in the much greater costs to current workers of the SSI and Medicare system. Because when they were founded pay as you go was easy: 20 workers to one retiree. Retirees only lived an average of 3 years after retiring. Now the ratio is 3:1, moving to 2:1 and the average age spent on the program is something like 15 years.
So if you are one of the brave 21st century workers you can expect much higher taxes to pay for all this. At best we'll have crumbling infrastructure, reduced spending in all other areas and weaker defense to keep the tax burden on those brave few young workers in line. At worst they will be worked like slaves to provde "promised" benefits to elders who are already (on average, and in many cases dramaticaly) richer than they are (or may ever be.)
20 year olds working at McDonalds in Compton to pay greens fees for rich retired dentitsts in Palm Beach.
Maybe that is fair and sustainable. Maybe not. Time will tell.