Batman said:
Don't we need to give the readers some credit for having a brain? I would hope they can figure out from a headline, picture, graphical element or context of the lede that they're reading a story on a high school sporting event.
I can see it if you're differentiating between something like a city and a county school (Podunk High beat Podunk Central 14-13...) or if it's a common name or the name of the city (Smith High beat Franklin High 14-13...) but I don't see how it's necessary each and every time.
But what if you have Podunk College and Podunk High School in the same town, which is frequently the case? Do you ignore it when it's Suburb High vs. Exurb High, both of which are in Podunk, too; in which case, your usage is inconsistent depending on the teams playing? And what if those graphical elements aren't online -- how are readers supposed to know that a picture ran with the story in print that made it clear?
A story should stand by itself. And a writer, especially when school names and mascots are so interchangeable at the prep and sometimes college level, should make sure to be clear, instead of relying on outside elements to explain basic details of the story.