Solution: Assuming we are not going to get rid of it entirely:
• The FICA tax should apply to all income no matter how much or where it comes from.
• Recipients should be means tested. If you do not need the money, you do not get it. We know how much everyone has made since they were 15. We know who is or should be rich.
• Eliminate payroll taxes to make American workers more competitive.

Result: 10 years after above solution becomes law:
• 75 year old grandmothers who have raised families and worked all their lives at low paying jobs will be called Welfare Queens driving Welfare Cadillacs by Republicans running for Office.
Result: 20 years after above solution becomes law:
• 75 year old grand mothers who have raised families and worked all their lives at low paying jobs will be called Welfare Queens driving Welfare Cadillacs by Spineless Democrats running for Office.
Result: 30 years after above solution becomes law:
• 75 year old grand mothers who have raised families and worked all their lives at low paying jobs will not exist, they will have died an early death due to homelessness and hunger.

A common misconception about Social Security is that it is a savings plan. Because you paid in you are entitled to get something back out. While certainly sold to the public that way, it is no more than a tax on current workers to pay a stipend to current retirees.

Considering your entire argument is based on this claim, you offer no support for it. Social security taxes go into a fund that is invested and used to pay future benefits that are based on the amount the retiree paid into the system. Perhaps you are basing your claim on the fact that the government borrows from that fund to pay other bills, so there is no pile of cash sitting somewhere waiting for people to retire. However, that money is borrowed and is to be repaid with interest, just as any other money that is invested. We would not like it very much if the government just took that money and put it under a mattress until we asked for it back after we retire. We expect them to invest it, which means lending it out to those who want to borrow (including the government itself). Now, that puts the government itself into debt, which isn't good, but that has nothing to do with the social security system which is separate from the rest of the federal budget.

But even ignoring that point, let me make sure I understand your argument:

1) Social security is more like a social welfare program than a savings plan.
2) Therefore, we should change it to be more like a social welfare program than a savings plan.

Isn't that a contradictory argument?