They have filters on the ACs but tell us not to do it to furnaces.
The intakes are small, but if the filtering media or screens are monitored and changed should not be a problem.
Just think of all the dog hair ingested and deposited somewhere in the furnace system or lint etc now.
We don't hear much about furnace fires ,though, in RVs.
There are different meshes of wire available. I haven't looked in years so I don't know about availability. A coarse grid would stop a lot of junk and no inhibit flow, if kept clean. This is the thing. They are afraid people would not clean them. Is there not a thermal shut down on furnaces to shut them down ff they get too hot?