I am responsible for game management at a small D-I university (but have worked at three other D-I schools, including a PAC-10 school) and I can tell you the administration and conference is even more so at fault because they encourage and allow it, ESPN just fuels the fire by showing it. Students think rushing the floor is a part of the game - if you win you get to jump all over the place and act like a buffoon.
My philosophy has always been that rushing the floor is a huge liability and I discourage it and do not condone it. I use the example of a high school kid in Arizona who was rushed on the court by his friends after winning a big game and had his aorta torn away by the impact (Google: Joe Kay, Tucson, AZ). No one means to hurt someone in the excitement but it can happen. Some conferences have rules that if your fans rush the court after a big win, your school is fined (Example:
SEC fined South Carolina this year) - now that can be a bit of a deterrent but I don't know of any other conferences that fine schools. So what if your administration encourages it? That's what has happened to me where I work. We have a railing between the student section and the court, there is a drop off of about 5' down to the court from top of the rail. We also have donors sitting in courtside seats about 4' in front of this section. Both of these things make for a great natural barrier to discourage the students from rushing the court (and it helps that we don't win much so we rarely have to deal with this problem). My staff is very good about telling the students to stay in their section and off the floor. Last year we had a big win when we beat one of the top teams in the conference (their star player was out that game with an injury) and the staff able to get the students to stay in their section after the buzzer went off - what happened next pissed me off - as the teams are leaving the court (a couple minutes had passed) our head coach goes over to the student section, gets the students all fired up and then WAVES THEM ON TO THE COURT! They jump over the railing, push aside some donors and jump around on the middle of the floor for about 30 seconds... and then they all wandered off. First off -
Bush League to wait two minutes (after ESPN had already gone to commercial) before charging the court, then it was like they had no idea what they were supposed to do once they got there
The administrators thought it was great for "school spirit" and there were no consequences for the coach. Now, like a pitbull that has tasted blood, they want more of it - every close game they get ready to make a run for it (luckily we lost a lot this year). Someone will get hurt, and Game Management will get blamed when it happens.
ESPN constantly showing footage of court/field rushes makes students think that's part of the college experience. Therefor, administrators think it's good for school spirit. It will take students dying before the NCAA will take action to curb this behavior. I just hope the deaths don't happen at my school.