Would it help if student pilots included "student" in their solo callsign?
Nope. Any pilot is entitled to caution, courtesy, and the right of way from every other pilot. If a "student" is flying solo, they are a pilot.
We don't all bow our heads and break off our established approach to get out of the way, when we hear the 20,000 hour old timer approaching from 25 miles out, nor do we needlessly coddle a student. If a student, or any other pilot, needs assistance, extra room, or is experiencing an emergency, they are most welcome to broadcast their need, otherwise, everyone follows the rules fairly. The rules for right of way work really well - if obeyed!