Earlier quoted context omitted.
Your formula has the opposite problem, by looking at cases that have a known outcome you are biasing results towards cases that end quickly (in particular cases that end in death). For a proper estimate we should look at cases where the infection is known to have begun e.g. a month ago. Then the mortality rate should be somewhere between dead/infected and dead/(dead + recovered).
> Your formula has the opposite problem, by looking at cases that have a known outcome you are biasing results towards cases that end quickly (in particular case that end in death). Unless I'm mistaken, that would only be true if cases that end in death are much faster than the cases that end in recovery. I have found it difficult to find detailed statistics on the topic, so I cannot tell you that it's definitely tru…
Bigger picture: lots of factors go into a good estimate, and epidemiologists are not new to mathematical modeling. When back-of-the-envelope math doesn't get the same prediction as the consensus models of what's going on, we shouldn't assume the epidemiologists are wrong.