By your analysis, and it is very good, SS will not run out of money. I say that is so because it is fed at an endless trough of government taxes, borrowings, or fiat currency. The system you describe is the 3 card monte played to hide the fact that is a simple tax and spend welfare scheme designed to generate dependency on the generosity of the Democratic Party.
If that's all that you got out of it, you didn't read what I wrote.
No, Social Security won't run out of money. But, the amount of money it receives (from all sources) will be reduced substantially -- and it will occur sooner than most people realize. Even worse, very few are prepared for what will happen when that occurs.
Without changes via legislation, Social Security will exhaust the Trust Fund around 2034, resulting in a 20% benefit cut.
There really isn't much that can be done, absent an immediate increase in payroll taxes -- to about 15% combined employer and employee rate (up from 12.4%).
If we wait until 2034, then a 16% combined payroll tax rate would be required.
Politically, a benefit cut is impossible. There have been some proposals to further means-test benefits (which are already means-tested... most don't realize it), but the proposed thresholds won't make much difference. The proposed thresholds would have to be drastically lowered, affecting most middle income retirees.