That's why I never had or ever will have a cat.
My dogs used the in/out swinging doors and did their business outside on gravel. As soon as I noticed a mess, I cleaned it up. Every year I would have "Regravel the runs day," which meant hours of me wheelbarrowing pea gravel to each run. Took 3 barrows full to fill each, had 7 dog runs.
As soon as I would dump a wheelbarrow full, the dogs would climb to the top and poop their biggest dump on it. Still prefer dogs to cats any day. They never scratched me or bit me for doing their usual upkeep.