They are very efficient if properly maintained. Cost and emission requirements likely have a lot to do with it.

Paper is much more effective at removing particles. However continue to use foam filters if you feel threatened by that cabal of lawn mower manufacturers who are secretly conspiring to empty your pockets.

Roadbike, thank you for your great advise.
You are a very wise man, indeed.

Some high-end mowers have a foam pre-filter before the pleated paper filter. In my experience, this makes the paper filter last forever since it doesn't get dirty.
The filter on a 2-cycle is extremely critical, because anything that gets through it goes directly into the crankcase. That's why they had oiled foam filters.
The old oiled-foam B&S filters were good too. I bought a Homelite/Jacobsen mower in 1990 with a 3.5HP B&S on it. I have given it to two sets of relatives since I started using self-propelled mowers in 1994, and I just picked it up from my brother and put a set of wheels and axles on it along with a general cleaning/fix-up, which included cleaning and oiling the foam filter. The engine has never been worked-on and doesn't burn or leak oil. The foam filter has to have some credit for that kind of longevity.

Thank you Saxman. That was exactly the point
I was trying to make.

Oiled foam filters do work for mowers just as the oil bath filters used in older cars would work. The air at the carb was cleaner than the air at the intake horn. However they simply are not as effective as a paper filter at removing the very small grit. The older oil based filters do clean the incoming air, but the newer filters take grit removal to another level. And they are not nearly as messy to maintain.

Some mowers still use those foam filters. My Bolens is only a few years old and it uses one. I agree, it is nice to be able to clean and re-use it, but I do trust the paper filters more.

Here is a link that might be useful: DIY Lawn Mower Repair Blog

Briggs has a brand new OHV engine that uses an oiled foam air filter.

Here is a link that might be useful: Briggs 550ex engine

One thing i have found---those small black plastic air filters with the pointed end, do sell a lot of mowers. I have gotten several trade-ins, and trash night finds, that ran good after i cleaned the oily goo off the air intake side of them. RJ

bought a craftsman with b&s motor last summer it had the faom filter / i have to clean it alot more than the older ones though