I'd like an interactive visual graph, for each country, along the lines of the Y axis is %age of population, logarithmically; X time since given number of <foo>, which can be adjusted externally, like the currently popular base of "since 100th case", but 'case' could be test/death/etc.
It'd then be primarily a stacked data lines/areas being (baseline to top) something like mortalities not obviously associated with COVID, mortalities with unconfirmed suspicions of COVID, mortalities ascribed to COVID (would be nice to split that up into serious pre-existing comorbidity), recoveries, individuals tested positive (not part of the prior two at that datum), tested individuals not yet resolved at that datum, those confirmed negative (at that time, does not preclude their retesting later) and then up to the 100% ceiling would be all untested individuals.
A dotted line can also be sent up there equating to total number of tests conducted (retested individuals would raise that figure higher above the cumulative "tested" results level, deaths without tests would drag it down a bit and it could eventually get beyond the 100% ceiling if there's a concerted effort in a given population). That's for current infection, but another trend-line for historic infection/immunity testing could also feature importantly.
Mark times of major policy changes (lock-downs/open-ups, whole or partial, etc) with handy markers.
And then, with transparency of layers, allow comparisons between two (or more?) overlaid charts. Could be countries, regions, continents, towns, global figures or single naval ship. Though with the smaller populations being noticably more granular you'd expect steeper lines to wipe out the untested+live upper section, as a consequence so that's one thing you should not be surprised to see..
Not all exact measures will be available, and some may be lagged, but additional markup can show this. On top of not having any hooe of knowing anything for sure for daily updates, so the most recent edge would fade into blurred extrapolation, ) countries with revising counts (as China appears to have done) or changing metrics (UK implicitly counting 'hospital deaths' only, but we could easily post-facto shove in non-ward deaths under whatever class best fits) are already back-extrapolatable to indicate what is and is not a blip like a single immutable line would suggest.
It all works in my mind, anyway. It's not so much the absolute figures we're supposed to take from this but the relative profiles (and thicknesses) of zones. An ahistorical Non-Covid Deaths area and/or practically invisible (even on log-scale) thickness of all Tested sections would indicate likelihood of any problems with a certain jurisdiction. (c.f. the Floridian counties, as mentioned, or those countries recently mentioned).