I suppose that you are going to tell me that taking them for a walk over the fields, teaching them to sit, beg, mew on comand and fetch is unusual too 
Unusual yes, unique no

Brendon loved a game of Fetch the Sweetie Wrapper, he could play it for hours.
All my cats have come for walks with me and whatever dogs were family at the time. Not just across fields, neither.

Early cats were taught to wait for their supper, just like the dogs. Somewhere along that habit got broken...
Mew on command - maybe not exactly, but all my cats respond(ed) vocally when spoken to. (It would have been rude not to, they said.)
Most of my cats travelled happily loose in the car; one also travelled with me and the dog in a light aircraft. ("Victor Tango, are you the menagerie?" "Affirm." "Report to tower on landing - bring cat." "Wilco.")
I've never needed to teach a cat to beg... rather, have tried to teach them to
not beg...

I never felt it practical (for me) to wipe feet and noses on entering the house, not for cats nor dogs, but that's just me. It has always been a source of wonder to me that a cat can walk through a carpeted hallway, up carpeted stairs and across a carpeted landing, and still manage to put wet muddy footprints on the bed, the loo, the bath... I always figured they must walk through the house on three legs, saving one dirty one for the territory-marking...
