I've currently got five cats (six up until one week ago) and all save one get up on the counters. We clean our counters before we cook anyway, and nothing is ever put directly on the counters (that's what cutting boards are for, silly) But, all of my cats are crazy about their hygiene. I always see Twilight cleaning, like, ALWAYS. And my Hershey pretty much cleans his paws when he's not harassing everyone else
My dad's cat Buddy, wakes up, cleans himself. Uses his toilet, cleans himself, etc. Cat's are vain creatures lol. Their nails are dirty yes, because the claws have recesses where bacteria, poop, urine saturated litter dust, can accumulate, but their feet themselves, between toes, their bodies, are constantly being cleaned