The whole idea behind SS was to call it "insurance" so as to not stigmatize the recipients because it was for one and all. We always had general welfare for the truly needy.
Means testing would just admit that it was, in fact, plain old welfare by another name. The wealthier would start to resent it; the poor would be stigmatized just like the old days.
Unfortunately this ain't the old days and welfare recipients are no longer stigmatized by it.