It has always been a pension plan, whether that was its theoretical purpose or not. Means testing could be an incredible moral hazard. If there is means testing, then it has to be an "F-you" amount before you lose benefits. I'd agree that someone with $20,000,000 is assets does not need the money. But someone who has scrimped and saved to get $1,000,000? Shoot, in conservative investments that's only going to be 30k to 40k per year. Why bother saving if SS will pay around that much for those that don't save?
SS is not nearly as in the hole as Medicare, but it is getting there. To address this, I'd Increase the retirement age by one month, for each of the next 24 years. There are studies that show how much this will save, and it is way more than you think.
Medicare is the real problem. It's already underfunded and the tax does not have a cap.