While I completely agree with most of what you wrote, there's one point to consider - there's a significant difference between homeowners insurance and retirement insurance.

That difference is that, as you allude to, the probability of a homeowner filing a claim is relatively low, about 5% in any given year, and the average payout is under $14k, so the average payout per policy per year is under $700.

Contrast that with retirement insurance (e.g., Social Security), where more than 80% of people who start paying in will reach their full retirement age (over 87% will live to age 62, the earliest age for retirement benefits). That means that most people who pay in will also file for benefits.

The average SS benefit is about $22k/year, and since the average life expectancy at age 67 is another 17 years, the average cost of payouts is (neglecting COLAs) about $373k. Divide that by say 45 years of paying into the program, and you get an average lifetime benefit cost per working year of about $8300.

This is what makes SS so costly for workers relative to homeowners insurance. It's the high probability of claims and the relatively high lifetime benefit amount.