Suppose we change it slightly: a Saudi prince wants to become a US citizen in exchange for some considerable investment into our economy. Do you find it objectionable? Because that's literally one of the available options today.

https://www.uscis.gov/eb-5

And schemes like these exist in most countries out there, it's not just a US thing.

There is no personal tax rate decrease in EB5 in exchange for the investment.

The point is that we're already selling citizenship for money.

In your original example, the only reason why it would ever make sense is if the Saudi prince in question can somehow produce more wealth for the public than they'd pay in taxes. In that scenario, it's exactly the same in the end, once you balance everything - you have sold them citizenship for money.

And if they don't pledge to earn you more than you'd save, then why would you even consider such a deal?

Would you call that "bullying" by the Saudi prince?

Yep. Definitely. This is exactly what Saudis do to US every time they can, like that 100B defense contract that made current White House into Saudis' faithful servants afraid to even mention Khashoggi or Yemen.