What's the point in getting worked up? It won't change anything.
Anyway, the reason that the King does not pay tax is that he is the King. Taxes get collected by His Majesty's Revenue and Customs before being handed to His Majesty's Treasury. He'd technically be paying tax to himself.
Your second paragraph IMO amply answers the first. This is precisely the reason people are getting 'worked up'. In any society with pretentions to democracy, this is a ridiculous state of affairs. And it's far less the financial implications that bother me than the total lack of accountability. Odd though it seems, the only institution with any ability to hold this people to account for their actions is MSM. And reading between the lines, its reasonably easy to deduce here who or what is being bought and sold, and at what price.
Windsor-PR is a formidable and very effective machine. Certain people throughout the duration of Elizabeth's reign have tried valiantly to take that particular bull by the horns. They failed spectacularly, on every count.
As to your separately made point, it's perfectly true that below a certain threshold you'll be tax exempt; above it, the property and assets will be tied up in trust with particular loopholes for tax avoidance. Note that no one has ever seen any good reason to close those loopholes. Nor do the overwhelmingly right-wing UK media ever seriously question why tax avoidance is perfectly legal, yet benefit fraud is a criminal offence.
Not too great a reach to arrive at an accurate conclusion as to why.