It's a pain in the ass, because the dog can't use the doggy door anymore. I have to leave the dog outside all day long while I'm at work, and then get up and down constantly to let her in and out to keep the cat from escaping into the great outdoor adventure.
I do that because I live in an area that is simply not safe for cats. The coyotes, hawks, and owls do a damned good job with the feral cat population. I know this, because there was a colony of feral "barn" cats living here when I moved in. I trapped, neutered, and released all of them. Without the constant breeding, they were all gone within a year.
Once they were gone, the rodent population exploded. The bird population has remained the same.
I am overrun with pack rats and bunnies. I've thought about bringing back some neutered barn cats from the local rescue operation to help manage that population; they take some feral cats that have been trapped, vaccinate and neuter them, and offer them as barn cats. The only reason I haven't done so is that I'm not happy with knowing that I'd probably have to replace them every year.
Meanwhile, the pet cat is forever locked in the house, which really pisses her off. She's always sneaking behind and under things, trying to charge the door when it's opened. If there were a SAFE way to let her out, I would. Bunnies beware.