:)
I'm only considering already acquired immunity from past infections. And I've given an example on how that's relevant. It's probably another example of polarization that you're assuming almost by default that I'm an enemy anti-vaxxer (I'm not). Oh well, nothing else to do that to keep talking, and hoping civilized conversation helps.
Rather, I thought you were interested comparing kinds of immunity. To to that fairly and well, you need to include the most common case: People's first infection.
Remember that most people's immune system is able to learn quickly enough that natural immunity takes care of the first infection without external help. The immune reaction doesn't start with the second infection, it starts as soon as the immune system starts learning. Excluding the first infection in an analysis seems very, very strange to me.
For the first infection, immunity acquired by infection doesn't exist yet, so for the first infection, that strategy offers an increased risk of death of 20× or more compared to vaccination.
For the second infection, the two strategies are roughly equal. Not exact, but the details don't matter, because...
For these two on average, immunity acquired by infection offers about 10.5× the chance of death. If the effectiveness during the second infection varies very much, then that number will be 9 or 13 or something, so who cares about that detail. The number 20 dwarfs everything else. The only way to make the two strategies comparable is to ignore the outcome of the first infection.
Note that 20 isn't meant as a serious estimate, it's a number I picked out of a hat. MUCH higher estimates are available. You may have read that 99.5% of deaths in the US are unvaccinated. If you start with that number and that two-thirds of the USians are vaccinated, then the number 20 becomes 400, and immunity acquired by infection is then roughly 200× as dangerous as the vaccines they use in the US.