IMO, if there was a broken valve floating around inside the motor there'd be all kind of ruckus and something imploding or exploding before you drove any 80 miles. I'm trying to imagine that valve head bouncing around in the cylinder and just letting you keep driving along with nothing but a flashing light on the dash...........seems extremely farfetched. If any valvetrain item breaks the car isn't going anywhere except to the side of the road pretty much instantly.......................discuss
If anything there will be a slight tick on that valve, they seldom close all the way if there is a seat issue, that creates excess clearance and noise.
The one time I've seen a broken valve in person, there was just a piece missing, like in the video below.
https://www.youtube.com/watch?v=xyY5xt4LmPw&t=341s
You are right though, there would be a misfire all the time, this isn't a "once in a blue moon" issue.