The OP clearly has no idea who might apply for the job. I would estimate that the public school educated numbers are close to 0%, since the recruitment is not pitched at the retired officers who would form the bulk of public school educated candidates. The job appeals to, and is pitched at, people who have had full career elsewhere first (usually in the armed forces) and who held an appropriate and current security clearance. The vast bulk of those will have served in the ranks.

That does not reflect the % of current diverse serving population of the armed forces, but the selection process is often skewed by those who apply for the job.

The OP seems to have a different agenda - so I will now depart this thread.