What would that chunk of money you annuitized be worth now if you had it invested in a S&P 500 index fund since 2013 (>13% annual return) with comparable withdrawals. I think you would have done a lot better than your fixed 7% annuity.
Most likely the money for the purchase would come from fixed income not money in stocks.
Therefore, the amount that is invested in S&P 500 in 2013 would not change, only the money invested in treasuries/money market equivalents would be reduced to purchase the SPIA.
So compare a 30 year treasury purchase reduced by the same payout as the SPIA annually and see when the treasury runs out.
Case Study:
A 63 year old and based on current 30 year treasury yields (4.89%, with 4.625 % coupon annually) versus a 63 year old male including 15 year payout to heirs if early termination of insured.
The answer is the treasury be exhausted after 22 years, while the SPIA last as long as you do with a minimum of 15 years.
For a joint 63 year old couple 10 year guarantee payout SPIA, treasury will last 26 years. An additional 4 years due to the increased cost (lower payout) for a joint insured.
I would also add that some may feel more comfortable increasing the amount that they invest in stocks knowing they have most of their expenses paid for by "guaranteed income".
Treasury bonds like SPIAs are not inflation protected.