The other problem with an annuity is that you don't get your capital back at the end! If you run the 4% rule in cFiresim you'll see that in the majority of 30 year periods you actually end up with more capital left (adjusted for inflation) than when you started!
This is even less of a problem, since dead people generally have very little use for money.
Or OP could spend some of the capital over time, rather than taking this all or nothing approach. Using Vanguard's nest egg calculator to see what might happen:
Assuming 60% stocks/40% bonds... retiring with social security sounds like age 65 to age 95, so maybe 30 years:
4% withdrawal ($12k/yr) lasts 30 years 91% of the time
5.3% withdrawal ($16k/yr) lasts 30 years 71% of the time
6.7% withdrawal ($20k/yr) lasts 30 years 46% of the time
Note stock allocation has less of an impact than you might expect. Using 80% stocks/20% bonds improves the 5.3% withdrawal scenario to a 73% chance of success, versus 71%.
Given the low fees in passive index funds, and the fact you get all of the returns with no insurance company middleman, it's probably your best option when the money is close.