That's a fair question because the harm takes a while to manifest. Let's take a small step back and talk about what an engine air filter does.
The air all around us contains dust, dirt, pollen, spores, etc. Some areas and times of the year have more contaminants in the air. The job of the air filter is to keep that stuff out of your engine. The benefit to car owners is obvious.
Now your engine uses a lot of air - like 12,000 gallons of air for every gallon of fuel - so the engine air filter has an essential job to do. When the filter gets full and can't hold any more dirt, all that air still has to get to the engine so dirt gets forced through the filter and heads on downstream.
The air flows pass the mass air flow (MAF) sensor on its way to the engine. The MAF sensor tells the engine control computer how much air is coming so the computer can send the proper amount of fuel into the engine to maintain the correct air-to-fuel ratio.
When dirty air is flowing pass the filter, detrimental dirt starts to build up on the delicate MAF sensor elements causing incorrect air flow readings. The computer then sends the wrong amount of fuel to the engine. This can rob power from the engine. But the harm comes from unburned fuel passing out through the exhaust system and getting caught in the catalytic converter leading to expensive damage.
A primary cause of catalytic converter failure is improper engine management, often triggered buy a dirty MAF sensor which was contaminated because the engine air filter had not been replaced as recommended. Car owners can buy several cases of engine air filters for what it would cost to replace a catalytic converter. So when it's time to replace your engine filter keep in mind the potential long term effects of putting it off. www.theautoanalyst.com