I'm no expert in SS, but I *think* the problem is part demographic and part political.
Back when it was set up, with 16 workers per retiree, and retiree's expected to live oh, say 4 or 5 yrs after retiring, on average, the system collected more than was necessary to pay the benefits.
Along came the baby boom, and when they started working enmasse, then SS was really rolling in the Benjamins. I think shortly after this was when the SS fund was mingled into the general fund (Nixon?) to help fund government spending. That was a huge political mistake I think, and probably reinforces your distrust of the system?
Now as the baby boomers retire, fewer and fewer workers are in the workforce supporting retirees (I think we are down to 3 to 1) and retirees are living longer and longer after retiring (I think we are up to 7 or 8 yrs, on average). I don't blame the SSA or the government for these demographic realities, but I do expect them to recognize them and make adjustments to ensure the system's viability, though not necessarily at current benefit levels for all retirees.
Your example 100K account probably isn't enough for a typical retiree. That's less than $15,000/yr for 8 yrs. What is that individual going to do after it runs out?