Nothing to do with the price of ice. Most high schools have to get a 2hr block for a game. They never use the full 2 hrs. Most coaches want the longer periods. The other thing they should do if they don't do longer periods they should have OT. 5 min 3 on 3 would be great for the HS game.
I think level of competition and education are the selling points. No kid is going to be sold over 9 minutes of extra game time. that relates to like 3/4 extra shifts a game. any kid playing for his HS that a prep is trying to get would in all honesty be taking a huge ice time loss going to prep. If he is being recruited them he is playing like 25-32 minutes a game in HS and all special teams
I went to a public high school game this week and honestly the resurfacing of the ice between periods took longer than the actual playing time. Zamboni guy was late getting on, had issues with his machine, swapped it out both intermissions with another machine.... Just add a few minutes and get it over with.