I'd also avoid going out if I was sick

You could be asymptomatic.

Vaccines reduce the load on the healthcare system by reducing the effects of the virus but if you look at the numbers (link at the bottom) fully vaccinated people can still need care. A general statement like your "the vaccinated, who would be running around asymptomatic" is cute but frivolous.

As of July 27 2021: "A growing body of evidence indicates that people fully vaccinated with an mRNA vaccine (Pfizer-BioNTech or Moderna) are less likely than unvaccinated persons to acquire SARS-CoV-2 or to transmit it to others." (https://www.cdc.gov/coronavirus/2019-ncov/science/science-briefs/fully-vaccinated-people.html)

We should just be living our normal lives.

Allow me to beat my current favourite drum: as of yesterday the 75% of people in Ontario with 2 vaccine doses provided 18.4% of the hospitalized and new covid cases. See the ink at the bottom. This means two things:

One - 81.6% of the covid cases in the healthcare system are from the other 25%, the ones living their "normal lives" or not fully vaccinated, and

Two - There would be more room in the healthcare system for people with 'normal' medical concerns if that 25% was fully vaccinated.

flu

The fatality rate in Canada from covid is about three times that influenza and pneumonia combined, over the last 20 years.

common cold

Can't find any numbers for people in ICU for the common cold.

Ontario healthcare numbers: https://covid-19.ontario.ca/data