No, the bacterial problem is true. COVID-19 causes massive bacterial infections in the lungs. Think of the green slime you cough out with the common cold, but deep in your lung. It's almost the same virus after all. The virus itself causes something else in the red bloodcells prohibiting the transport of oxygen, but this is unlikely the major letal problem.

Covid-19 is a coronavirus, the common cold is usually a rhinovirus. They're not 'almost the same virus' as you assert, they're completely different virus families [1].

For starters, coronaviruses are enveloped, and rhinoviruses are naked.

[1] https://en.wikipedia.org/wiki/Virus_classification

15% of common colds are caused by coronaviruses. https://en.wikipedia.org/wiki/Common_cold#Viruses

Sure, and that’s why I said “/usually/ a rhinovirus”.

But saying the common cold is “almost the same virus” as coronavirus still isn’t true as a blanket statement: the vast majority of common colds (up to 85% by your stats) are a caused by completely different virus family.

Viruses don't usually do any damage to the body. It's the immune system's response to virus that causes damage. The immune system releases chemicals into the blood stream (inflammation) and the increase of these chemicals in the blood reduces oxygen transport. If left unchecked, these chemicals can cause sepsis, and the lack of oxygen causes organ failure, and that is how a virus becomes lethal. These inflammatory chemicals produced by your immune system are what gets trapped in the lungs as pneumonia, which causes other issues. So controlling inflammation and reducing the viral population is the key to survival.