A very small portion of Social Security benefits go to the wealthy, so excluding them from the program would save little. In order to save a meaningful sum through means-testing, Social Security would have to “means-test away” some or all of the benefits of many middle-class retirees – those with household incomes starting at $50,000, many of whom could not afford to forgo their Social Security benefits. Moreover, if Social Security stopped paying benefits to upper-income seniors, political pressure would mount to have it stop collecting contributions from high earners as well, which would hurt the program’s finances. Or, if means-testing were implemented so as to require high earners to keep paying but get little in return, Social Security would become more like a welfare program, which Americans would not support.
In short, it makes far more sense to leave intact the current system’s fair and intelligent design, whereby everyone pays in, and everyone receives their earned benefits. A more detailed fact sheet is available here.