SARS-Cov-2 is a distinct virus that causes a distinct disease: COVID-19.
Virus influenzae is a distinct virus (or a term for a small group of similar viruses) that causes a distinct disease: seasonal influenza or "flu."
This is why you can compare death rates of SARS-Cov-2 and influenza virus, or COVID-19 and flu.
"Common cold" refers to a group of various viral infections of the nose and throat, which can be caused by at least 200 different viruses. This means you can't compare death rates of a diverse group of diseases called common cold and a single disease, such as COVID-19 or flu.
When a common cold extends to the lower respiratory tract, it is, by definition, no longer called common cold, but laryngitis, bronchitis or pneumonia, for example.
When a person gets a common cold that becomes complicated as pneumonia and dies from it, the cause of death is recorded as pneumonia not as a common cold.
If you stick with a definition of common cold linked above:
Common cold is a self-limited contagious disease that can be caused by a
number of different types of viruses. The common cold is medically
referred to as a viral upper respiratory tract infection.
...then you can't even say that common cold is deadly.