With room available in the healers hut or hospital, villagers with Small Pox or other contagious disease continue to run about doing their normal business, so they spread it very rampantly. They are not self quarantining or heading to the healer. They need to avoid roads and make their way to the healer right away.
There is also an issue with victims of bleed-out. They die way too quickly and villagers near them who are busy will not stop what they are doing to help. Instead, if someone who is not busy is tasked with the job of retrieving their wounded souls, they will be too far away to be of any use. This needs to have the same mechanic as a burning building, but I dive into more detail in another post which I will link here. Please expand the view to see the full idea as it involves educated users and military training.