AG:
In answer to your rhetorical question: Yes. Of course America needs a Queen.
Their closest thing to royalty, The First Lady, was an abysmal failure when Melania, whose sense of humour was such that she adopted a Transylvanian accent, took the powerless reins of state from Oprah...it was Oprah, right?
But back to your question: yes, but with certain conditions.
Since the last President walks and talks like a 'professional wrestler', and this did seem to appease the orangeophilic throngs, 'Queeny' must be trained as one and be able to leap from a turnbuckle, execute the flying scissors and use a tiara like a ninja uses a shuriken.
Queeny's meetings with the President should be televised as a ringside reality TV show with Dr. Phil providing compassionate psychotherapy in between rounds in alternating corners.
What about a Ref you ask?
Mirth McConnell immediately comes to mind...after all I don't think Disney will mind freeing him from his Star Wars character Admiral Gial Ackbar gig.
Even better, both Sylvester Stallone and Arnold Schwarzenegger could be the trainors, highly adept with the spit bucket...saved of course as prized antidote to Covid 19.333... Alpha-Omega-Centauri variants.
Perhaps Dr. Oz, who is not a wizard BTW, as ringside doctor would add credence to Her Majesty's role.
None of Queeny's or The President's interactions can be scripted, otherwise it wouldn't be real, would it?
If a President wants to overturn an election?
He gets an 'attitude adjustment' moonsaulting scorpian deathlock.
Pack the Supreme Court with supernatural-worshipping Inquisitors?
The Tombstone Piledriver seems to be the only sensible royal response.
If the President finds himself caught up in a state of perseverating prevarication?
A Macho Man Randy Savage Flying Elbow to the windpipe will do nicely, thank you very much.
Of course no self-respecting US Queen can ever borrow any of the wrestling moves made famous by the Windsors: The Saxe-Coburg-Gotha, The Wallis Simpson or the Epstein, let alone own a kennel of crotch-sniffing, guest humping stumpy-legged cattle dogs.
I'd watch that show!