Enclosure fan with Air purifier installed?

Just wondering if anyone has looked at if the enclosure fan should be installed when you have an air purifier installed. Seems the enclosure fan does not come on automatically when the air purifier comes on. Since it does not come on the air purifier is forced to pull the air through the off fan (causing it to spin). This im sure will prematurely wear out the enclosure fan and add resistance for the air purifier fan.

With the air purifier, is the enclosure fan even needed?

I keep both and sometimes run the enclosure fan only when I need slow air flow, such as after lasering to clean the enclosure from smoke. Sometimes I run both if I want to get some extra flow while keeping the air purifier on low (purifier on low to decrease noise, but enclosure fan on to add extra flow a little).
I get your point about running against resistance, but I think the effect is too little on the fan and not really a big deal.