Why a week ago? If it takes longer than a week for victims to die, in a situation with rapidly increasing infections that will give a very distorted number.

The best source I found on the subject -- a disease modeler with CDC who was giving an interview -- said that their current estimates used 5-day doubling, 15-day median time to death, and 1% CFR to do their estimates.

For the modeler, the purpose was estimating the true number of cases (which they estimate as current_deaths * 800 for a first-order approximation) -- but similarly, you could use that to estimate CFR by taking (num_cases / 8) as the denominator. Except, of course, that you can't realistically estimate num_cases. With the exception of Diamond Princess and possibly South Korea, everybody's numbers tell you more about the number of tests they run than the number of infected that exist.

One doctor from John Hopkins, for example, estimated that there are between 50k and 500k cases in the US as of 3 days ago -- and my own admittedly-amateur estimations using CDC numbers for deaths from influenza and all-cause pneumonia could only set an upper bound of ~400k cases as of March 1st

Sure, maybe just one week is too short and it needs to be longer. But that just makes my point stronger, doesn't it?

Using the total number of people infected today means they're including a bunch of people who may go on to die, but they're not including those deaths yet. So they're making the death rate look smaller than it is.