IMO, it's all situational. If we beat Alabama (I know they are away this year, just for example) in a come-from-behind last second drive after recovering the onside kick to win the game as time expires. Yea I rush the field.
If we just play a good game and in the second half pull away from a team, no, because we won like we wanted to.
Plus, now that I have kids and they go to the games with me, I dont think I would ever rush the field, and if I got that vibe(that ppl were about to), would leave a little early to insure their safety. And we don't ever leave early, regardless of the score.