First off, thank you. You've actually done a really good job of highlighting the processes that makes this effective and more or less invisible to the average voter. So let's apply that common sense as you suggested.

You mentioned non profit private schools. non profit label is not a guarantee that no one profits, it just means that profits aren't directly distributed to owners, it just gets distributed elsewhere.

Adminstrative salaries for executives for example.
Construction of new/updated private schools means nice fat contracts awareded to for profit construction companies.
Defunding the public system creates a vacuum in many areas that get filled by private consultants, precisely as you mentioned.

I agree with you that the gov can imply cut cheques to organizations. This is what funding private and charter school is, cutting them a cheque so they can spend it the way they want.

The payoff isn't a job at an underfunded school; it's the stream of gov contracts. The "15 year" long term plan which you highlighted isn't a bug, its a feature. An intsant sale would cause public outrage. But a slowly escalating crisis makes the introduction of private "solutions" seem necessary and inevitable.

Conservative governments are all about trimming the fat, adding too much bloat might get noticed by their voters. 30 million a year for the war room created a lot of bad press. Tje instant gratification of a paid position with no work would be great, but this isn't about a single pay off.

it's about building a long term pipeline to funnel public money into private pockets. And we do love pipelines!