But to others, the purchases are legitimate investments and nothing unusual for a future king.

To some, the spending is a sign of hypocrisy and a threat to Crown Prince Mohammed bin Salman's legitimacy. The reports come on the heels of his anti-graft campaign, which culminated in the detention of Saudi princes, officials and businessmen at the Ritz-Carlton in Riyadh.

Saudi Crown Prince Mohammad bin Salman's goal to diversify Saudi Arabia's oil-based economy and transform the kingdom into a tech and logistics hub could ultimately be an opportunity for American enterprise.

The 32-year-old crown prince is a polarizing figure who has captured the financial world's attention. First in line to succeed his father, King Salman bin Abdulaziz, he is spearheading Saudi Arabia's economic transformation plan and has overseen an invasion of Yemen, a blockade of Qatar and a domestic crackdown on graft that has swept up high-profile royals.

This is not a guy who is going to Monaco and dropping $100 million on gambling. ... That would be a very different kind of story.

First, the paper linked Crown Prince Mohammed to the record $450.3 million auction sale of a Leonardo da Vinci painting, "Salvator Mundi." The following week, the Times traced the mysterious $300 million sale of Chateau Louis XIV in France to Crown Prince Mohammed. The paper also noted his roughly $500 million yacht purchase in 2015, reportedly a spur-of-the-moment splurge.

As such, his every move is dissected by Middle East watchers for signs of turbulence in the world's second-largest oil-producing nation and pre-eminent Sunni Muslim power. This month, a pair of New York Times investigations gave tea-leaf readers plenty to talk about.

The Saudi government declined to comment about the chateau to the Times, but has disputed reports that a Saudi royal purchased the da Vinci on behalf of Crown Prince Mohammed.

In light of the anti-corruption arrests, the chateau and yacht purchases send signals that are inconsistent with Crown Prince Mohammed's social and economic reforms, said Robert Jordan, former U.S. ambassador to Saudi Arabia under President George W. Bush.

"The lack of judgement and the lack of self-awareness that this reflects I think is shocking," he told CNBC's "Squawk Box" on Wednesday.

"There will be members of the royal family, others in the community, who are saying, 'Wait a minute. This guy is just the biggest hypocrite in the world.' So, I think he's got to be very careful to balance that," said Jordan, now an adjunct political science professor at Southern Methodist University.

But others say Crown Prince Mohammed's spending habits and his corruption crackdown are separate issues, and those who conflate them might fuel misconceptions about public opinion Saudi Arabia.

Crown Prince Mohammed is trying to rein in widespread corruption, not discretionary spending by the future king, said Bernard Haykel, professor of Near Eastern studies at Princeton University. He says Saudis don't consider splashy purchases to be corruption, nor do they typically object to wealthy princes investing in assets with tangible value like overseas property, yachts or artwork.

"This is not a guy who is going to Monaco and dropping $100 million on gambling," Haykel told CNBC on Wednesday. "That would be a very different kind of story."

While Western media are focused on the purchases, the average Saudi is more concerned about the introduction of a new value-added tax and the ongoing reduction in fuel subsidies, said Haykel, who recently traveled to Saudi Arabia. These Saudis worry that their incomes will not rise to meet higher costs.

Haykel says wealthy Saudis who say they built their fortunes through legitimate channels are "ecstatic" that Crown Prince Mohammed cracked down on allegedly corrupt princes and officials. They see the type of corruption he is targeting, like bribe-taking and skimming funds for development projects, as a burden on the system, Haykel said.

Still, Haykel says Crown Prince Mohammed has not clearly communicated his motives for the crackdown either at home or abroad.