The other influence is the evolution of the virus itself. A longer lasting less-than-lethal infection is, in the long term, is selected for by evolutionary pressure.
In the short term though the biggest selection pressure on the virus is vaccine evasion.
Longer lasting, sure. Less-than-lethal (or otherwise less harmful), not necessarily. Whether the host dies a few weeks after contracting the virus is not really relevant for transmissibility.
Actually, several viruses have evolved to become deadlier:
In the short term though the biggest selection pressure on the virus is vaccine evasion.