I don't use my DK for cutting - at least not yet. I grow about 90 acres of hay and sell it as it stands. The buyer brings his own gear to cut/bale/haul. This keeps me from investing thousands in the gear but still provides a nice check.
I do, however, use my tractor for spraying and routine farm maintenance and have therefore spent a number of continuous hours in the fields. The pre-screens do their job, so they do require being brushed off at times. For me, this has not been a big issue - just something I remember to check. Your situation may be far different than mine.
I must admit, this being my first tractor, I hadn't even thought of this problem before I saw it the first time for myself. Having said that, I would suspect that all tractors, at least to some degree, have the same issue. I further suspect, smaller(lower) tractors are worse.