That’s the whole point of a rolling average. Downside is if there’s a big uptick one day, it doesn’t fully reflect in the rolling average.
I don't see how knowing about a single day's uptick is of any particular value in this instance. When the cause of death is violence, then an uptick has correlating data that makes accuracy of daily reports important. But with an illness of indeterminate time, and a myriads of variables in each individual's illness, a 3 day rolling total is a little more relevant, IMO.