Oil bath filters are quite efficient, and were very common in the olden days.
The air passes down through a wire mesh and over the oil bath which splashes oil up into the mesh, trapping dirt, which works its way down into the bath of oil where it should sink ..... the oil gets pretty dirty in dusty climates, and the advantage is that renewing the filter is only a matter of cleaning it, and tipping in a pint of engine oil.
So called air FILTERS are primarily intake air SILENCERS. There's a LOT of noise comes out of an air intake, especially diesel engines because there is no throttle - the intake is wide open all the time. My first car had no air filter or silencer. Ford Popular 1172 sidevalve. It was a noisy thing. As people got more fussy about creature comforts, they wanted extras like ... a heater, and a lot less noise. Also, engines needed re-bored several times in the life of a car, which was great for the motor trade. Adding air silencers and air cleaners probably doubled the average live of an engine's bores.
Modern motoring almost never require a rebore, or de-cokes and grinding-in valves. Those were routine jobs in the old days. I can still do it.
CharlesY