What if the disease never evolves? What is the fallout for Europe and the rest of the world?
The bacterium Yersinia pestis does seem to be a recent evolution (from non-flea borne Yersinia pseudotuberulosis). Genetic differences suggest a divergence some 1.5-20 kyears ago. It LOOKS like there were some 3 major steps to change a relatively benign 'pseudotuberculosis' into the Bubonic plague. So even if the two lines diverged some thousands of years ago (which isn't certain in the first place), the length of time that the other changes took seems to be uncertain.
The articles I read suggest that the first reasonably certain evidence we have of Y. pestis is in the Justinian Plague in the 6th century, and the timing of the evolution of the bacterium fits this being (one of) the first outbreaks of the disease.
So. Let us suppose, for the sake of argument, that the last mutation in the bacterium doesn't happen then (or possibly ever).
We're suddenly looking at a PoD possibly in the 5th century or even the 6th, so it's not 'geological depth' and thus ASB.
The first major effect would be to remove the Plague of Justinian, which would have HUGE consequences for the Roman Empire. Without the plague, the East might have held onto the Justinian's (re-)conquests in the West, and the Balkans wouldn't have been depopulated resulting in the Slavic influx and replacement. Most of the Balkans might have stayed strong, and Illyrian might be one of Europe's major languages ...
In the short run, the Roman Empire is far stronger.
In the long run, however, new diseases arise and spread. There would have been nasty pandemics later, if not then, and if not the same disease.
There would still have been some 'Black Death' that wiped out 10-50% of the population of e.g. Europe, but with a different disease, and in a different century.