Thanks everyone for the responses. They have helped to clarify the details of a SPIA. A SPIA has some nice features, but other detractors which make it not appropriate for me. Let me explain the financial product that I am looking for. I don't know if this exists or not. If it does, hopefully one of you will tell me.
Imagine 10,000 people all the same age as me who each have retirement savings of $500,000. Each of them wants to retire now and based on their spending level and expected market returns, this is enough to support them if they live for their expected lifespan. However, if they are lucky and live to 105, they will run out of money. All of them put their money (a total of $5 billion) into a trust which invests the money in some combination of VTSAX, VTIAX, VBTLX, and VTABX. Note that they are exposed to market risk. There is no insurance company involved. Then, each of them receives a payment monthly for the rest of their life (but nothing left for their heirs). This payment is based on the expected life expectancy of the individuals still alive and expected market returns. The trust should be fully depleted at the death of the last member.
In this manner, the individuals are still exposed to market risk. Additionally, if the whole cohort of 10,000 lives longer than initially expected (i.e. medicine causes a 10 year increase in life expectancy), then they are at risk. However, they are insured against their individual life expectancy. So they only need to save enough for median life expectancy rather than 95% percentile.
Also, note that there is no insurance company involved causing counterparty risk or taking a nice fee off the top. Instead, the design is a mutual, each member is insured by the others in their age cohort.