A Math Check
Let's really check the math here on contributions. I'm going to make a series of assumptions that don't match with American history, but I think are none the less reasonable and make the math straightforward.
If in 1960 you started your career making 15K/yr, you could have just finished a 45 year career. (I know that people did not make 15k/yr on average in 1960, but the inflation of the 70's severly distorted pay, so stay with me). Every year you receive a 3% pay raise and at retirement you were making 56K/yr which is in line with the average salary in the US right now. You contribute 6% of your pay to SS each paycheck (it's actually slightly higher.) The government is saving 6% interest on that money (that is lower that most of the last 45 years, but higher than right now.) All that money invested and growing is worth ..... $300,000 when you retire. Note that the interest alone on that money ($18K/yr) is almost enough to cover your monthly check without touching the principle. Add to that the folks that kick the bucket before they can enjoy SS very long and this doesn't look like such a bad deal for the government. The issue with the SS "trust fund" is that the government paid it a very low interest rate. If you were buying treasury bonds, you would have something like the numbers above.
(For those of you at the beginning of your career, this calculation should prompt you to immediately start saving a significant portion of your salary. It is very reasonable to expect to do better than 6% by taking reasonable risks with your money.)
But SS is not a savings account. It is an entitlement program so that we don't have a lot of indigent old folks. SS isn't retirement money, just enough so that people can eat and afford minimal housing. It has been very successful in that respect. The cash flow into and out of SS can also be balanced with a few small changes if we make them now. For example, salary above $90K is exempt from SS. Removing this exemption would make up a lot of the projected future shortfall. Changing the retirement age by a year or two could make a big dent. Adding a slight amount to the tax rate also solves the problem.
The real issue is what do we want to do as Americans about our social safety net. In the 50's, we had American children dying of starvation just like you see in Somalia, etc. We as a country decided that that was unacceptable and we implemented the school lunch program so that children got at least one solid meal a day. Result: No more starving kids. (Fat ones, yes, but that is another thread.) SS, Medicare, Welfare, Unemployment benefits, etc all form the minimal safety net we provide because in the past, we have collectively said we don't want the US to look like a third world nation in some places while being extremely wealthy on average. We are more generous than many countries, less generous than most industrialized countries. The level of generosity is where the debate is centered these days. There is a significant faction, prehaps even a majority, calling for less benefits to ease the taxpayer burden. There is a significant faction trying to hold the line. The question to you is "what should our country look like and are you willing to pay for it?"
Re: A Math Check
The cash flow into and out of SS can also be balanced with a few small changes if we make them now. For example, salary above $90K is exempt from SS. Removing this exemption would make up a lot of the projected future shortfall. Changing the retirement age by a year or two could make a big dent. Adding a slight amount to the tax rate also solves the problem.
Removing the salary cap will actually worsen the problems with SS unless there is also a means test also put on the entitlement. If you just eliminate (or raise) the salary cut-off under the existing system you also end up increasing the monthly check you pay out to those same people and, in the long run, since the average retiree collecting SS collects more than they pay in you end up with a short term increase in revenue and a much larger long term liability.
Changing the retirement eligibility dates should be done automatically IMO. It can be done by tying it to the average life expectancy estimates just as current COLAs are tied to inflation rates.
All of your suggestions together won't eliminate the problems though - it would put the problems farther down the road but they don't go away that easily.
The "rich" do not receive more from SS than they put in when you consider the time value of money. (See the above calculation.) While those who put more in do get more out, it is not proportional. But I agree, let's cap the payout. The purpose of the program is not to provide a comfy retirement, it is to ensure a minimum standard of living for those approaching the end of their lives.