Billy, I heartily endorse most of what you say - but have to disagree with this:
Of course there are disinterested parents who send their kids to boarding school because it’s easier
In my (entirely current) experience there is nothing easy about either the entry process or the day to day reality. I am admittedly talking about a 'major public school' which operates only full boarding.
Registration, that is - registering an interest in applying - has to happen before the child is ten and a half. They then take a pre-test (which is now the definitive entrance exam) in year 6, at which point they may be offered a conditional place, put on the waiting list or rejected. Those with a conditional place then prepare (if at a prep school) for Common Entrance, another exam, at the end of year 8. They will also have visited at least three boarding houses - and it is the housemaster, rather than parents or child, who choose which boys they will accept for their house.
Full boarding fees can now be close to £45k per year. We don't know anyone who can pay this amount for five years without a thought. We do know of A list celebrities and international oligarchs who cannot get a place at the school, despite pleading and inducements.
Not everyone pays, of course. Around 20-25% of pupils receive some level of bursary - after their parents have been closely interviewed, filled in a long, and gruellingly intrusive application form detailing their financial background, and submitted to a home visit to ensure they have given an accurate representation of their circumstances.
Then the child takes up their place - and their family spends the next five years haring up and down the motorway of flung about in planes and trains, both for purposes of general support and interest but also to pick up and drop off for the never-ending round of exeats and holidays.
If any part of this is easy I haven't yet stumbled upon it!