Out-to-Lunch
Thinks s/he gets paid by the post
You have to provide basic personal info (or I’d have verified), but it appears you can still buy COLAd annuities. They cost about twice as much for the same starting payout.
https://www.immediateannuities.com/immediate-annuities/annuities-and-cost-of-living-adjustments.html
https://www.annuity.org/annuities/riders/cost-of-living/
I was imprecise in my terminology (and RetiredHappy was not!). She referenced inflation-adjusted annuities, which is what I MEANT to reference. Instead I conflated COLA and CPI-adjusted.
AFAIK, there are no CPI-adjusted annuities available. The immediateannuities site you provide only has options, as far as I can tell, for a fixed percentage increase.