I always thought of an air filter as a life extending product. Kind of like eating healthy and not smoking. But since race engines run hard and fast, and almost always get rebuilt at ridiculously short mileage intervals, then why not let them enjoy a bacon cheeseburger and smoke a few while they are doing their business?
So, on my street cars and push truck, definitely. On my race engines? no, I just make sure the scoops are pulling clean air and no salt or dust gets in under normal operation. I also try to make sure no big chunks of stuff can get into the turbo impeller. So far I have never had to replace a turbo because of compressor damage. I always ruin them long before they get to that point by ejecting hot valve parts through the exhaust side first.
Also, keep in mind that we run alone, never in packs and never directly behind another vehicle. That is the condition where lots of crap gets kicked up and ingested by the trailing car. I would definitely run a filter on any engine where you may be following another vehicle.
Also, I run a turbocharged, inter cooled engine. My complete intake tract is a convoluted set of passages and tanks and what not. It would be very difficult for a solid mass of any size to make it to the engine. N/A guys have a different set of conditions.
Just my opinion, YMMV