I dont know a lot about the diferent branches of TKD. My first TKD class was Moo Duk Kwan. It was a small class and outside of ITF WTF or ATA. That particular schol offered Muay Thai and JKD. The curriculum was different as well as the approach to sparring, which was more intense than I had previously expereinced. a few years after I left that class, I joined a ATA school. I never fought any matches with them, but there sparring sessions were based on points. Head kicks being worth the most, as you mentioned. However, after a point was scored the match was reset, and actual contact seemed to be frowned upon. Thats not to say that all schools train this way, however, TKD is fast becoming a sport dominated art and its destroying its original purpose.
The Moo Duk Kwan class had plenty of hand strikes as well as stand up grappling. Knees and elbows were also used. At its core TKD can still be a fighting art but the majority out there is no longer. Instead its soccer in Gi's.
Now thats the right way. Less patterns but more involvement with key movements. Certain patterns always work well, like a 1-2 punch. Isolate these smaller aspects, teach them opnly and allow the students to develope certain habits or patterns themselves rather than burying a few jewels in a maze of stances and flowery movement. Encourage a students crativity and adaptability rathern than say "Do this this way, because this is the way its always been and thats right".
"When I let Go of who I am, I become who I might be."