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).
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 true or not, but I agree that it's an important variable that should be taken into the equation.
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.