I personally have stormed the court back in the day.
I support court/field storming. HOWEVER....they need to protect the players and coaching staff. Look at NCAA, they have state troopers with the coaches protecting them.
fans are so close on basketball courts, they are basically storming as time expires and players are still on the court. at least with football, they have to run all the way from sidelines onto the field, so football has slightly less issues with injuries
basketball...they need to wait 5-10 seconds and clear the road teams