Flea-catching cat flap

Almost every cat gets fleas at some point. Some of them get fleas all the time. And they absolutely hate being treated for fleas. Yet almost every cat lives in a house with a cat flap allowing them to go in and out without human intervention, and most cats love nothing better than attempting to squeeze through very small gaps. So, let's give them very small catflaps, and impregnate the surrounds with some sort of anti-flea chemical, held in a stiff brush-type material. That way, whenever the cat goes in or out, flea-repelling chemicals are automatically brushed into the cat's fur. It's better than ordinary flea treatments, because the cats love it, and the fleas never even get a chance to start breeding in the house. This idea could perhaps be extended to getting the cats to wipe their muddy feet on the way in, so that we don't have to clean the floor every half an hour. Perhaps the deluxe model could contain a small footbath for them?