I'm not saying you have an odor problem, but there is a smell, and all cats, even the best behaved with perfectly maintained litter pans, have it. Cat owners become habituated to it. I've been catless for enough years that I can detect it, again, and once more have that sixth sense that all non-catpeople have that enables me to walk in any household, detect that faint whiff of ammonia, and know in mere moments that a cat lives here. In turn, the resident cat(s) will detect my mild allergy to them. That is when they attack.

With one or two cats the scent isn't bad. I just wondered what it was like with a dozen of them.

I think dogs smell much, much worse.

I know a cat that will only drink water out of a bathtub. He will get in the bathtub and complain (meow) until the tap is turned on a trickle, and then drink from the running water.

Emphatic agreement, here. I have never noticed a cat to smell unless it was ill or unable to groom itself.
I have had two cats (neutered males, unrelated) that if you buried your nose in their fur, smelled slightly of sulpher. IMO, what you are probably smelling (amonia) is a less-than-sanitary litter box, and that is the owner's fault, not the cat's.
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And baking soda really does work in kitty litter. Doesn't take more than a small handful, but we need it with a male (neutered, but even so) kitty around.

And Blaze the he-kitty has rather an inclination to tongue-kiss, but we don't let him. He does have this very endearing gesture of opening his forepaws out to embrace you about the neck if you pick him up or if he wants a body-ride.

Spooky, our she-kitty, is a fetch-cat; she will bring us paper wads to throw so she can pounce on them and then bring them back to throw again. Wadded-up grocery receipt tape is perfect for this. She'll play fetch or kitty-hockey and clearly enjoys the heck out of it.