I mean the easy fix is to remove the cap on Social Security income. You don't pay into social security on income above $150k.

In general, social security's problems are because the system was constructed to assume unending working-age worker growth. That year's payouts are funded by that year's takings. With the boomers retiring and the birth rate going lower, you just get to a demographic point where there are more people cashing out than paying in. Compounded of course by real wages declining.