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.
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?
https://www.uscis.gov/eb-5
And schemes like these exist in most countries out there, it's not just a US thing.