I don’t see why you think that’s true - if infections are latent long enough to spread and it’s virulent enough, with a fatal outcome, it could rapidly wipe out most people. There’s no reason to believe a viral infection that mutates from an animal infection to human wouldn’t be both easily transmitted and highly lethal. It’s not a great evolutionary adaptation for the long term, but transitory effects can often be sub optimal and catastrophic.

COVID is a perfect example. It could easily have been significantly more lethal and it was very infectious in its first blush with humanity. What process other than luck prevented it from being both highly lethal and highly contagious rather than moderately lethal and highly contagious?

If you have a reference to a first semester immunology text that supports this supposition I’m very interested to read the justification. Otherwise this feels like a big of an appeal to authority.