1. They're lousy air filters
The K&N (within the industry they're called "gauze" because they're based around medical gauze mesh, you know, the stuff they wrapped around your wrist when you hurt it playing football) air filter and all its copycats (BMC, Emgo, and others) are crap. The K&N company stated out in a Kawasaki dealership that developed a great race-day (flat track, initially) filter that enjoyed success. But it should never have been taken prime time. As a street product, it is a failure. It's one thing to rely on a product for one or two races, and not care about its effect on an engine you rebuild every few races. It is completely another thing to apply this to a machine which is expected to go 60,000-80,000 miles without needing engine top end work. I consider this kind of marketing bordering on criminal.
The extra airflow K&N air filters are famous for gets there through HUGE holes in the filter mesh. The industry standard procedure (established by automotive companies in the 1940s) for testing the condition of a pleated paper air filter is to hold the filter up to a naked 60 watt incandescant light bulb. All the light should get through. A good paper air filter does this. A bad paper air filter blocks some of the light. And a K&N? Not only can you see the light, you can see the light bulb!
Foam air filters are not much better than gauze, and have their own issues. First, not all the foam is the same. The dense dark gray stuff used in some foam air filters is actually more restrictive than the stock paper air filter. And of course the foam air filter requires oil treatment (as does also the gauze) which is seldom performed correctly, that is, uniformly, with the correct type of oil, and frequently repeated. The result is the foam filter rots out.
2. Both gauze and foam air filters foul Wing carburetors
The aforementioned oil migrates downward and enters the Goldwing's air chamber and then the vacuum piston area of the carburetors. If this were the only negative associated with gauze and foam air filters, it would be enough for me to avoid them. But it's not.
3. The gauze air filter progressively becomes harder to clean
What happened to K&N's 100,000 mile warranty? I don't know. I suspect it was offered only to car users anyway. But I know this: at some point the gauze air filter becomes un-cleanable. Even when you use the company's own cleaner (mandatory, as detergent will not do the job), in a short time the filter reaches a point where the dirt does not come out.
4. The foam air filter is not really very serviceable
Not only is the foam air filter a lot of work to clean correctly (see my video), requiring as it does a handful of cleaning stages including solvent, then detergent, then clean water and either hot or moving air (not compressed air), but at a point in its life cleaning actually destroys the foam air filter, causing it to disintegrate. Foam air filters are also hugely over-represented in air filter fires on powersports vehicles.
5. Gauze air filters are harmful to the engine
The gauze filter flows more air by flowing more of everything, dirt included. You don't believe it? It is widely known in the industry. Shops having experience with gauze filters on sport bikes know to check for retarded cam timing (which lowers cylinder compression) due to worn cam chains (the first thing to wear in an in,ine four's crankcase, but obviously not something that will show up on a Wing). Also, OEMs routinely ask the K&N question when vehicle owners call them asking for warranty assistance with prematurely worn engines. The durt gets into the cylinders, and into the crankcase.
In short, the pleated paper air filter that came stock in the four cylinder Wing (and its Taiwanese aftermarket copies) can't be beat. It does the best filtering job, matches the carburetors best, does not foul the carbs, requires no maintenance, and does not harm the engine.