The short answer is yes, of course they do.

Racers and serious recreational riders who ride every day can wear through tires pretty fast. I used to regularly wear my tires down to the threads when I was a broke teen racer. Many tires don't live this long because the sidewalls get cut or damaged before the rubber is entirely worn down. Nowadays I've got other things to do than ride my bike 3 hours a day. I replace tires when of these happens: the rubber tread is approaching being worn through, or the casings get damaged.

Tires can also give up simply from old age. Rubber doesn't age well, and neither do cotton casings. Heat, UV, ozone, etc will destroy tires over time. This is definitely a concern if you have a fleet of bikes.

If your tire looks like a snake that swallowed a mouse, replace it immediately. That's the classic indicator of damaged casing and the tire will soon blow out.

Also, in my opinion it is a very bad idea to rotate tires. It's OK to move the front to the back, but not vice versa. Don't put that old bashed up tire on the front. Front tires should be perfect and as new as possible. Font blowouts will usually cause a crash. You don't want that. Put the old worn out or booted tires on the back if you're a cheapskate.