My kids have had no ID trouble when flying alone, but if there has been any question, their school IDs were fine when under age 18.
The only time I've been required to go to the gate with them was when they were flying as unaccompanied minors, only when they were quite young, maybe under 13. Although I did not leave the airport until the plane departed, I don't recall anyone enforcing that rule.
Enjoy your trip!