Your assertion that rats weren't involved in the spread of the black plague is misleading.

Rats do spread disease. Some experts believe they were not the vector for the black plague, but there are several other (many of which are quite recent) outbreaks where rats have unquestionably spread disease.

Take a look for yourself:

https://www.cdc.gov/rodents/diseases/direct.html

Personally I believe we should preserve human health over rat health, and a good way of doing that is to exterminate rats.