I went into that calculator and it does not say anything about inflation... Do annuities get wiped out by inflation (i.e. they'll keep paying me the agreed monthly amount, but unfortunately it's not going to be worth much)? If, then they're pretty crappy.
Yes, they generally get wiped out by inflation. You can get annuities whose payments increase by a fixed amount every year, or that increase based on the performance of the S&P 500 or whatever, but AFAIK you can't get an annuity with inflation-indexed payments today. I agree that that limitation makes them pretty crappy. Inflation-indexed annuities used to be available (I think until 2010 or so), but companies broadly stopped selling them because hedging long-term inflation is expensive.
In the UK at least it looks like you can still get inflation index-linked annuities - for example, there are entries in the Hargreaves Lansdown "best buy" tables for for RPI-linked annuities: https://www.hl.co.uk/retirement/annuities/best-buy-rates
But their starting income is less than half the income from the non-increasing annuity, presumably because of difficulty/expense in hedging inflation risk.
There are instruments at least that used to exist (in the UK) called defined benefit pensions that effectively work as you describe. They have some level of inflation cap (typically between 3 and 9%) beyond which they are not inflation protected. I don’t know if people can still get them, but many pensioners in the UK on private pensions have them.