Is a provision that gives a lesser punishment for self-reporting reasonable?
Yes.
The Iowa State Board of Education has ruled that it is a reasonable exercise of a board's control of student conduct to give students who self-report their good conduct violations a lesser punishment or even a chance to avoid all negative consequences by making some sort of restitution. In re Anderegg. 14 D.o.E. App. Dec. 107 (1997). https://www.edinfo.state.ia.us/web/appeals_float.asp?book=14&decision=107