Nope, not the King. He might have a lot of stuff, but quite a lot of that is basically unsellable. So his crown might be worth a gazillion, but parliament would probably interfere if he tried to sell it off. And it would be an issue what is actually his to sell and what is really owned by the state.
All the revenue that the Crown Estate generates is given directly to the UK government to use, so they get plenty of tax from it already. ~$400 million in 2022 for example.
The british royal family are a bit like a church, Not that rich on paper but buffalo buffalo buffalo owning so many assets all over the world that if you did the legwork to put it all together they might turn out to be richer than the richest oligarchs.