It's not the worst plan. One of our cats tells my wife it's time for her to goto bed at the same time every night by climbing on the arm of the couch next to her and just staring at her until she goes to bed. Then he takes her seat and naps next to me until I go to bed about an hour later, at which point he often moves to the cat tree, depending on where the cat that doesn't care about sleep hygiene is.

Not every cat cares about bedtime, but their love for routine is really funny.
The other cat likes to be let into my office at about nine so he can sit in the window and bird watch before my meeting at ten. Yesterday my schedule was off, so I wasn't in there at nine but was still in the kitchen getting caffeine. Poor buddy was screaming at the door for me to let him in, and was shocked when I came to open the door from the wrong side.

If you want to be woken up at the same time every day regardless of whether or not you will it or how much sleep you’ve had, a cat is a great way to accomplish that 👍

-running on 5 hours of sleep because I went to sleep too close to kitty breakfast time

Speaking from experience, cats will absolutely bully you into a routine.

Depends on the cat! You'd want to set up the routine first so the cat knows what the routine should be. Otherwise the cat might think random is bedtime.

Or you might get a cat like mine who cares not when bedtime is, just that it happens so she can cuddle.

Kinda. It makes life easier living with a cat if you go to bed at the same time every night.