Well, you're one for two on this.

Steve's right on infection-mediated immunity: the CDC study is the crappy one that doesn't agree with the global consensus. You can find data from Qatar, Israel, the UK, etc. all indicating that previous infection, even considerably earlier than vaccines, are all at least comparable to two doses of the mRNA vaccines.

If you have the background to walk through the science, I'm happy to do so. I don't want to waste the time unless it's going to be meaningful to you. But the CDC study uses crappy data narrowed down to a small sample size which it then needs to correct using linear estimators of nonlinear relationships, all to get a conclusion that scarcely even meets common sense, let alone is more trustworthy that the other literature--I can go through this in more depth if you like. In contrast, the countries with national health care systems have vastly better data, can do matched samples, and show sizable levels of protection.

On the other hand, Steve's way off on the death rate. Not quite two orders of magnitude--certainly not with Omicron!--but it's hugely wrong pre-Omicron (seriously--more than 0.01% of the population of the country already died!) and probably still significantly wrong for Omicron-only...and anyway, the real point is that the risk is highly age- and comorbidity-dependent, and any discussion about death needs to take this into account. You can certainly find populations for whom the death rate is 0.01% or less (e.g. 10 year olds)! The discussion about how to address the pandemic should absolutely take this into account.