Waiting after meat before milk comes from a concern of either the taste being still in your throat or particles still in your teeth and you are eating that with milk. Do we apply this in other cases as well? I can think of lots of other potential applications.
For example, if you eat chametz meat (not just cooked in a chametz pot, I'm thinking something like chicken with breadcrumbs) on the morning of erev Pesach, and it's now after the time when you can't eat chametz but your 6/5+/3/1 hours have not yet elapsed, are you allowed to eat anything?
Or similarly, if you accidentally eat meat that's not kosher, do you have to wait before eating anything?
Or if you eat a korban close to the end of its time period and it's now after that time, do you have to wait before eating anything else?