Pets don't brush their teeth. Do they ever get tooth problem?

I know I should brush my cats teeth, but I don't. It's hard enough clip[ping claws. I'm not entirely sure Chelsie realize her teeth are gone. If she gets ahold of a large piece of food, she will try to gnaw at it like a normal cat, but without teeth she risks choking on it. And when she goes outside with me she tries eating grass, but with no teeth she doesn't get any where.