I don't think this is as widespread as people believe. Certain locales tend to be overwhelmed at any given time, but I don't think that's the case for the majority of hospitals in the country. Unfortunately I don't have any statistics.

>But hospitals are currently overwhelmed with mostly voluntarily unvaccinated people

This has been the narrative for a while now, but as vaccination rates increase the ratio of vaccinated:unvaccinated hospitalized patients is approaching and surpassing parity. And some not so recent government data from the UK[0] (I haven't seen any media report on it) suggests that for a number of age ranges, vaccinated individuals have a similar death rate per person-year, i.e. vaccines are not doing nearly as much as claimed. This data is pre omicron.

0. https://www.ons.gov.uk/peoplepopulationandcommunity/birthsde... - check table 7 in the spreadsheet. Maybe I'm misinterpreting something?