@Dennis-aka-Denji
The issue, as far as I understand, is that rats aren't actually all that keen on migrating.
A rat's nest is usually extremely confined in its territory to allow the spread of the black death at the rate it did actually spread.
So having an outbreak of the plague in one town shouldn't affect a town two miles over, since rat populations generally remain fairly close to their respective nests.
Rats certainly didn't help the matter, but it is not without skepticism that they are the main contributing factor in the fast spread of the black death across europe.
Equally, it's not even without contention that the black death was the plague to begin with.
Here's a paper that is casting some of the skepticism on the theory
https://pmj.bmj.com/content/81/955/315