Indeed as you and another commenter pointed out correctly, it is not the whole picture, and given an intelligent, evil design one could possibly create a disease that spreads fast and kills only much later (by let’s say, causing cancer). But fortunately we are not inside Plague Inc.

But if I am not mistaken, from a strictly evolutionary perspective there is no pressure towards such a disease — a genetic variation that is more deadly won’t dominate over its less deadly variant and thus deadliness could be a variable that only changes randomly from the initial level (and decreasing if it is actively detrimental to spreading, where I would say that in case of a human population deadliness does correspond with fear).

But IANAE, nor a mathematician.