> 1) About half of those people in hospitals were vaccinated.
Considering Ontario is 90% 12+ fully vaccinated and 85% 5+ fully vaccinated[1], this means somewhere in the neighbourhood of say 15-18% of the population represents 50% of our hospitalizations, likely a lower percentage, since as you note this tends to hospitalize people in older cohorts.
> 2) Vaccine mandates do not considerably improve vaccination update, especially among elderly who benefit the most from vaccination.
Firstly, Ontario's elderly are massively vaccinated. 80+ is 99.99%, 70-79 is 99.99%, 60-69 (which I wouldn't consider elderly these days) is 97.37%.[4] This isn't due to anything very recent either, the rates have been 90%+ two doses for the 70+ crowd since August of last year.
Secondly, if this were true, you would not expect to see upticks in vaccinations coinciding with mandate implementations. Yet in [1], in November of 2021 you see a clear uptake in vaccination doses administered. This coincides roughly when 5+ were authorized for vaccination[2], as well as when federally regulated industries began requiring it.[3]
You can see from the raw data in [4] first doses between Nov 1 2021 and Jan 1 2022 was 468,443 for 5-11s, 28,257 for 12-17s, and 220,641 for 18+. Nearly a third of all first doses during the time period when 5-11 just became newly able to be vaccinated came from Ontario's adults. There was an 88.5% vaccination rate among 18+ at the start of that time period and there was a noticeable dip in vaccinations due to the holidays (you can see this in the booster #s too). You can question the motivations of those people but I think the numbers at least suggest that the mandates do have a part to play in driving people to get vaccinated.
[1]: https://covid-19.ontario.ca/data
[2]: https://www.ctvnews.ca/health/coronavirus/covid-19-vaccine-e...
[3]: https://www.canada.ca/en/transport-canada/news/2021/10/manda...
[4]: https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=171000...