You may not see a fully-fleshed-out graph for whole countries or even states/provinces, because not everybody reports complete data like this, and not every location which reports data does so in the same way. So, a "lumped" data display might not be at all meaningful.
However, these sorts of numbers/graphs are available for some areas, which you might (or might not) be willing to accept as reasonable exemplars. That is to say, if a certain region has X number of cases, Y hospitalizations, and Z ICU patients, and Q deaths (all for COVID-19 of course) you could calculate the percentages and relationships. Look at a dozen sets of data from around the country, compute and average-out the percentages, and that's probably a good set of numbers to use for the purpose of extrapolating to country-wide numbers.
I'll get you started with one such - my own county.
https://www.sccgov.org/sites/covid19/Pa ... board.aspx
This page has links to a lot of graphs, including the number of new admissions per day, number of patients hospitalized (total, ICU, and non-ICU), and so forth. I think it provides just the sort of detail you're asking for.
The raw data which underlies these charts can be downloaded from https://data.sccgov.org/browse?category=COVID-19
I don't know for sure, but I suspect that similar data is probably available from a bunch of other local jurisdictions in the United States, and probably Canada as well.
So, if you want answers... the data is out there. It won't be perfect or entirely complete, but it should be good enough for study and reasoned discussion.