For those of us bothered by moulting cats…
Get hold of one of those small vacuum cleaners, the ones that are pretty much useless for anything else. Wire the cleaner so that it switches on as the flap is opened.
Arrange a section of the hose in a loop around an existing catflap aperture. Make a longitudinal slot in the hose and blank off the end, so that, on entry (and exit), all of that surplus fur, skank, rotten leaves, mouse entrails etc are removed from your furry friend.
You still have to brush down the apparatus weekly and remove the bag of course (unless your cat is valuable enough to warrant a posh, overpriced Dyson). It may also deter foreign cats who aren’t prepared to brave the blowdry on the offchance of some extra rabbit’s liver biccies.