They weren't regarded as police matters, rather failures of the flight schools' systems. No instructor authorisation. An example of insurance excess considerations. I agree, a departure from the rest of our discussion.
CASA's legal definition, per Part 61 (so not RAA) of a "pilot" means "a person authorised under this Part to manipulate the flight controls of an aircraft during flight." When solo, the student is the pilot, the only person, the only pilot in the aeroplane. So, yes, the pilot in command.
In CASRs Part 61 and Parts 141/142 (which don't apply to RAA), an instructor has obligations in approving a solo flight by a student. Then off they go on their merry ways, nil obligation to supervise the flight. On completion of a flight the instructor would take an interest in what was undertaken for the training records of progress.
Instructors do like to sit on the bench outside with a radio and observe a first solo (and listen to radio calls).