Why can't a swamp cooler and a furnace be active at the same time?
As long as the heat is turned off the air handler fan can be run while the swamp cooler is running.
Swamp coolers work on evaporation the water flowing over the plates causes the cooler and more humid air then the blower pushes this into the home.
Folks may think the fan on the furnace air handler can’t be run because you don’t heat and cool at the same time.
When I lived in Ohio back in the early 80’s one place had a swamp cooler and the way it was set up the furnace could not be turned on.
I added a fan switch to turn on and circulate the furnace air handler and our unit was much cooler.
We had an office party at our place and the next week I was fixing all my coworkers units and eventually all the units in our block. I got a few attaboys from senior enlisted as it made the units much cooler and back then AC was not available in enlisted housing. So I think it may be the way it was set up the thermostat only had heat or cool. I came from the west coast and had been involved in building several housing tracks and had only seen 1 swamp cooler in my life so I did not know it was unusual and added the simple toggle switch to turn on the fan but the thermostat still controlled the gas valve and would turn the fan on if the switch was in the off position.
So possibly because it has always been that way and many did not know it could be done.