They weren't just to treat and cure victims. They also had to bury the dead and keep tally of the casualties in the public record. For that, they had to move all the time from house to house. As they were always on the move, they had to wear durable leather boots. The ones they wore were similar to the ones our workman's put on their feet.
These black leather shoes would go almost around the knee and would have the same wax coat on it, like all the other clothing of the doctor. As they were at risk of contracting the disease the most, they had to get that even on the boots to make sure the bad air doesn't stick to it.