a controversy.. but speaking about the smaller, low cfm engines
there might be some advantage of installing an air filter on a small marine engine but it should in no way replace the flash suppressor screen that should be there.
(the flash supressor is the screen that prevents the flames from shooting back into the engine compartment in the event of a backfire... and possibly causing an explosion. an air filter shouldnt be depended on to do this)
I personally have not seen any advantage of an air filter, but I have seen the disadvantage when a paper element becomes damp, swells and then causes restriction in the airflow.
I have been around boats and on the water all my life and I know of a couple boats with original engines that are approaching 70 years old that have never had an air filter on them and they still run in top shape... and many more that are at least 50 years old and still in top running shape..... all original and without air filters. both inboard and outboard engines. (but then, there may be other areas of the country with dirtier marine air than we have here in the west)

I have also seen big fancy boats and runabouts that are less than 15 years old that have air cleaners installed and some of the owners have had to rebuild their engines and others have trouble with keeping their engines running....
it all has nothing to do with whether an air cleaner was installed, but has everything to do with how they are maintained. I dont care who ya are, I will argue that there isnt much dust floating around the marine environment of the type that is critically harmful to an engine, so in my opinion there is not much point in adding an unnecessary bit of equipment to keep out what isnt there to begin with. But there are others that will disagree. if timely oil changes and proper maintenance can get you 70+ years of good steady use and lack of it causes premature failure, then someone if going to have to prove to me the benefit of an air filter on a boat engine before I will tell anyone its a good idea to install one. but im not telling you that you shouldnt either.....
so it comes down to whether you want one on your engine or not...