Air Filter

I have a 1998 Chevrolet Silverado with a 350. I've been curious because people say that it is bad to run with no lid on the airbox. I tried it once and it gave me some power and sounded nice. I put my lid back on. I'm looking into an intake but I just wanted to know anyway why it was harmful to the engine or if it was bull. My filter clamps right on my intake so no particles can get in. The only thing I can see is I'd have to clean my filter more often. If anybody knows why or if people are full of crap I'd like to know.
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Don't mind the animations. I was bored.

The only reason the box has a lid on it is so you can change the filter
and the air coming into the filter is from the outside of the engine compartment. Cooler air will make the engine more emission friendly, but also restricts the airflow, so when you take the lid off you get hot air from the engine compartment but you also get more unrestricted air. I would check out K&N filters they have a freeflowing filter set up with a reusable filter element. A little pricey but they guarantee more horsepower. http://www.knfilters.com/FIPK/fipk.htm