I have that many cats. In fact I thought this thread might be about me when I first saw it (then I remembered I don't have any friends
).
I have 25 or so permanents/semi permanents and normally an extra 6 or so fosters. The most I ever had at one go was 56. At that time I was trapping a colony of 60 plus cats and needed somewhere for them to recuperate for a few days post neutering before being re-released at site. As it happened I was having my bedroom refitted, so it was completely clear and I had relocated to my living room for the duration. So I put the building work on hold and filled the bedroom with hospital baskets. That was a one off though.
My house does not smell at all. I have had an outbuilding built for my very temporary fosters, and other, slightly longer term fosters are in a separate room in my house.
I have also had a cat toilet extension built with a good extraction system and a door with a cat flap into it, and from it to the outside. That is where the main litter trays are. Many of the cats use the garden of course and I have made a large area of soft earth for them to use.
Everything in my house is designed to withstand that number of cats, from the flooring to the furnishings.
I end up keeping cats that have little hope of ever being adopted, mainly because they are old/have health problems or are unfriendly to humans/semi-feral. As someone said upthread - few people actually want to have this number of cats. In an ideal world I'd have two. But the choice is either take them in, have them put down or leave them to die/reproduce on the street. The choice isn't even to take them into your home or to leave them in cages at the shelter. As those cages at the shelter won't stand empty. The minute they are emptied they will be filled again. It just means that more cats can be helped. Sadly those that will still only be a tiny fraction of those that need the help.
For as long as people think it's ok to not neuter their cat, or it's OK to buy kittens from someone on their street/Gumtree/whatever, this situation will never improve. All the rescuers can do what they can, but still only a fraction of the cats that need it will ever be helped.
I only keep cats permanently that like other cats. And they all live happily together - forming bonds and sleeping together and showing no signs of stress. Of course it would be nice to be able to devote more time to each one (although the semi ferals wouldn't thank me for it) but it's either live in a house with a little less attention or die on the street.
My 'disgusting' house is pictured (they particularly like the kitchen - i had underfloor heating installed just for the cats). In the second photo the cage is for a cat that is being introduced to the household.