Any kind of air filter inevitably restricts air flow into the engine. That's why on some out and out performance machines you see bell-mouth air intakes going direct into the carbs. However, no air filter means that any particles floating around the air get into your engine, where they can act as an abrasive.
As Dicky says, you can get filters that restrict air flow less than paper filters, but this inevitably means that they also allow slightly larger dust particles to get in. If the engine is being stripped down regularly, as in racing cars, this doesn't matter, but in a road car this eventually leads to a build up of dirt in the engine, some of which gets into the oil and circulates around the engine and some gets burned onto surfaces in the engine.
I once fitted a twin-choke Weber carb to an engine. The original huge air filter box didn't fit the Weber, so I had to replace it with a 'pancake' air filter sitting on top of the carb. This worked fine until one cold winter night when the engine started faltering on the M1. On pulling in to Woolley Edge, near Leeds, I discovered that ice was forming around the body of the carburetor. The original filter box had a warm air intake, but the 'pancake' filter was only getting cold air and the moisture was freezing in the venturi!
