Man, have you guys never landed early and proceeded to sit at the gate while the airport scrambles to find people to actually move the jet bridge into place? Just because you land on time doesn't mean that you're getting off the plane on time.
No, that specific thing has never happened to me.
I've had medical emergencies where they ask for a doctor, i've had a broken door and a broken toilet delay takeoff, I did have one stretch though where American kept cancelling the flight out of Pittsburgh the night of. So I'd get a text in the middle of the night to have to change my flight to get in that day. And one time we landed too early and the flight out of the gate was still there, so we had to sit on the runway.
In my experience, the most at-risk delays are mid-day flights. As long as the flight out of Pittsburgh is early and the incoming flights was from the night before, then there would likely be no risk of a takeoff delay out.
But, like all things, you remember 0% of the times that it everything runs as expected and 100% of the times that it doesn't.