As someone who has worked with/been associated with a squad for several years. Coaching belief was that they didn't want the team score out publicly because they didn't want other schools in the classification or region to know specifics about how they did. (IE: Podunk doesn't want Smalltown High School knowing they scored a 197.) Why provide bulletin board material or anything to help the opposition beat you?
Because cheerleading is based upon judging, and there can be so much politics when it comes to judging, coaches want an advantage. And while I'm sure fans from many squads video other schools in the region so their squad can see what the competition is doing, many don't wan videos posted publicly because of a fear parts of the routine may be stolen.
There are rivalries in cheerleading just like anywhere else. Some are under the surface but exist nonetheless. There are also politicians who also coach. Coaches are going to protect themselves and their squads as best they can.