Yeah, first realised this when it became clear that all the "breakthrough infections" (with the 0.1% rate for fully vaxed) were actually "breakthrough hospitalizations" and that the US was not actually tracking the former consistently.

For the second point I guess it depends on the jurisdiction, there was a nice chart from the CDC in an Ars article indicating how you should still expect a relatively higher rate of vaccinated people in hospital when the vaccination rate is high (and also less people in hospital overall!).

https://arstechnica.com/science/2021/08/pandemic-of-unvaccin...

In Ontario they are quite open about most details, you get breakdowns like what you describe daily and a nice dashboard from the science table.

https://www.cp24.com/mobile/news/ontario-sets-new-multi-mont...

https://covid19-sciencetable.ca/ontario-dashboard/