Social Security as it currently exists is not a welfare program. It is an insurance system (the actual name of the program is Old Age and Survivors Insurance -OASI) . Anyone who pays into the system for more than the minimum numbers of quarters (40 eligible quarters) is eligible for benefits when they reach retirement age. It doesn't matter if you earned the minimum amount or were paid millions of dollars per year. If you paid into the system and live long enough - you get your benefits. It doesn't matter if you are a billionaire, or a pauper.
When you add "means testing" it is no longer a retirement program, then it becomes a wealth transfer program that "taxes" one group (the successful) to support another group (the unsuccessful).
You're quite right in that Social Security is not an investment program. It is a compulsory form of federal insurance the singular purpose of which is prevention of abject poverty during a worker's retirement years. The FICA (Federal Income Contributions Act) paycheck deduction is commonly referred to as a
tax, which for most participants turns out to be a windfall because the eventual
payout usually far exceeds the amount
paid in.
The overall effect of Social Security has thus far been a vast improvement in the general quality of life in America because it has eliminated the shameful kind of impoverished misery that existed before the program commenced. If it becomes necessary to impose a means test on upper income level recipients it will not occur as a total disqualification of all participants above a certain net worth or income level. Rather, there will be measured reductions of payouts based on individual net worth and income level.
For example, I would qualify for a reduction in my monthly allotment -- probably around ten or twenty dollars, which isn't going to "punish" me because I have a generous pension and some savings. If I were worth more my reduction would be proportionately more. If I were a multi-millionaire I would receive nothing from Social Security -- because I wouldn't be negatively affected by a loss that I wouldn't even notice. But the upside of such a means test exercise would be prevention of eliminating Social Security payouts to some less fortunate seniors who can barely afford the bare necessities of life.
Essentially this is a moral issue which is backed by government muscle -- which may be said for a lot of FDR's actions and policies.
So I would need to be a greedy, miserly sonofabitch to oppose the imposition of a Social Security means test if it becomes necessary to sustain the program.