Rather, the tax is extremely progressive due to the various "bends". As you contribute more into the system, they make the per-dollar value of your contributions go from .9 to .3 to .15.
Anyway, Social Security is fine. It's Medicare/Medicaid that's going to nuke the budget.
0-147k: 12.4%
147k+: 0%
The number goes down at the higher income bracket, which means you pay less % of your money in payroll taxes the more you make. That is the very definition of regressive.
That aside, as a matter of policy, uncapping the taxes would destroy the popular notion that the amount of Social Security you receive reflects your contributions. If the public believed it was literally just income tax, and if there was no cap there would be no reason to not just adjust the income tax by that amount, it would be subject to the same politics as income taxes and could be cut on a whim. Treating it differently than income taxes, even when it is not, is essential for its survival. If they didn’t cap it, top income tax rates would be >60%, and there isn’t much appetite for that.