Since the publication of his memoir, Spare, many have speculated about whether Prince Harry was properly vetted for drug addiction or illegal possession of controlled substances when applying for a US visa.  According to the memoir, prior to his marriage to his American wife Meghan Markle, with whom he now resides in California, he used cannabis in the UK and California and cocaine in the UK. When a foreign national seeking entry to the United States admits to using controlled substances, this can trigger criminal and mental health related grounds for inadmissibility. Prince Harry, however, is likely not subject to the standard security and background check measures because, we theorize, he is traveling on an A-1 Head of State visa.
Who can use an A-1 Head of State visa?
An A-1 visa is appropriate for members of royal families. As stated in the Code of Federal Regulations (CFR), “a nonimmigrant alien who presents a diplomatic passport or its equivalent shall, if otherwise qualified, be eligible to receive a diplomatic visa” and this specifically includes “members of a reigning royal family.”  Prince Harry is a member of the British Royal Family. So, he is a likely A-1 visa holder.
Moreover, there is a category of highest level members of a country's public leaders called A-1 Head of State, for which Prince Harry could qualify as a member of a royal family, for which he need not be a "working" royal or even a "working" government official. Most A-1 diplomats need to be coming to the United States on behalf of their national government primarily to engage in official activities for that government. But a Head of State meets the eligibility for an A-1 visa “regardless of the purpose of the visit to the United States.”  They can travel to the US just to visit or do any activity, even work-related. If he is on an A-1 visa, Prince Harry does not need to be coming to the US solely to work on behalf of the British government.
Why is it significant that Prince Harry is on an A-1 Head of State visa?
A-1 visas have a lower security and background check threshold. Only the terrorism and national security inadmissibility grounds of the US Immigration and Nationality Act §212(a) apply. So US consular officers only would vet Prince Harry under the ineligibility grounds found in INA §§ 212(a)(3)(A), (3)(B), and (3)(C).  He would not have been vetted by the US Government directly for mental health ineligibility like drug abuse or addiction or for criminal grounds of ineligibility like a controlled substance violation. Mere admission to drug use in a memoir would not keep Prince Harry from staying in status and being able to renew an A-1 visa.
Does Prince Harry need become a US citizen or green card holder to stay long term in the United States?
Prince Harry does not need to become a lawful permanent resident or United States citizen in order to reside in the US. He can remain on an A-1 all his titled life. He just needs to be vetted under the terrorism and other national security grounds from time to time. Each time he visits, he is welcome to stay for an indefinite period called “duration of status.” He does not need to be a working royal to stay in A-1 status. He can stay as long as he remains a member of a royal family.
 BBC: Prince Harry's drug use and his US visa: The duke's other court case explained (6 June 2023). See also Mirror: Prince Harry COULD still get US citizenship despite drug confessions in book, says lawyer (7 April 2023)
 22 CFR § 41.26. INA§101(a)(15) defines all “non-immigrants.” Among those are Class A-1: “[A]n ambassador, public minister, or career diplomatic or consular officer who has been accredited by a foreign government, recognized de jure by the United States and who is accepted by the President or by the Secretary of State, and the members of the alien's immediate family.” INA §101(a)(15)(A)(i).
 Diplomats and Government Officials (A-1 and A-2), US Embassy and Consulates in the United Kingdom website.
 Diplomats, International Organizations and NATO Employees Overview, US Embassy and Consulates in the United Kingdom website.
 22 CFR §41.21(d)(2).
 To illustrate, students are also granted duration of status (D/S) as their period of authorized stay, each time that they enter the US. Inevitably, they graduate, and fall out of status if they do not leave in the United States.