Just because I'm having nostalgia for the days when it was all about Social Security, let met briefly explain what price indexing instead of wage indexing would do to the program.
First, only the initial level of benefits is indexed to wages (which rise faster than prices), after that annual COLA increases are linked to prices.
Second, while the formula for Social Security is complicated, benefit payouts are somewhat progressive, with poorer people getting a bit more relative to what they pay in, and higher income people getting a bit less, but there is a relationship between lifetime income and benefit levels. Higher income people get more.
Changing to price indexing would, over time, delink the relationship between income and benefits entirely. The formulas in place would lead to poorer people having their benefits rising in real terms (over and above inflation) slowly over time, but benefit levels for higher income people would essentially be frozen. In about 90 years or so every Social Security beneficiary would end up receiving essentially the same level of benefits, which for higher income people would be a tiny percentage of pre-retirement income.
While Social Security isn't meant to provide the complete retirement portfolio for everyone, it is meant to provide a reasonable chunk of pre-retirement income for poor and middle class people so that all people, including victims of either bad fortune (stock market crash, major health care bill, etc...) or good fortune (living longer than expected), can aspire to maintain their pre-retirement existence.
Pretty pictures here.
...minor correction, this discussion is about progressive price indexing, which continues to index low income benefits to wages while stopping it for high income people. Pure indexing would just continue to reduce everybody's benefits, relatively to current law.