The unvaccinated aren't overloading the healthcare system, the majority of covid cases are in the vaccinated.

In the Canadian province of Ontario, over 75% of the population are fully vaccinated and they having a high surge of the Omicron variant. According to this recent daily report from Global News, the cases among the vaccinated are a lot higher than the unvaccinated: https://www.google.com/amp/s/globalnews.ca/news/8492247/ontario-covid-cases-january-6-coronavirus/amp/

In the article, it says that a total of 13,339 were reported on January 6, 2022. 10,648 were in the fully vaccinated, 1,797 in the unvaccinated, 452 were partially vaccinated and 442 were unknown vaccination status. This article also reports the number of people in hospital with covid, 2,279 people are in the hospital with covid but even the amount of hospitalized covid cases the fully vaccinated are higher than the unvaccinated. 1,156 hospitalized patients are fully vaccinated, 123 are unvaccinated and 96 were partially vaccinated.