I tried, it does not work that way if you think. Or at least your “population” spec should be not arbitrary current administrative region or country, but specific virus spread area, which is very difficult to get data. You’ll get weird absolute numbers for EU minicountries (San Marino and Luxembourg are top) and very different figures per China, Hubei and other regions there. And if you finally compare in graphs you’ll have same graph anyway.
I guess it depends on what you want to do. If you're trying to make sense of a given countries response, (cases) / (population of administrative region) seems like a decent metric. Also since policy tends to follow administrative lines it's a decent (but extremely noisy) metric to see what policies are working.
What do you want to learn from (cases) / (people in infected area)? The denominator seems difficult to define since it's not scale invariant. If you defined an "infected area" as being within 1 km of an infected person, for example, you'd get a very different answer from if you defined infected area as 10 km from an infected person.
In the limiting cases where you define infected area with very fine or very course granularity, you get an infection rate of 1.
It doesn't even change the intercept because bigger countries reach their threshold number of cases sooner so that shifts them back again. Hence most of the lines are all roughly on top of each other regardless of country size.
