plasibility check:an american monarcy ?

Doubtful. Republicanism was proving very strong by this time in the minds of the Americans and they were fearful of a strong executive like the king represented.
 
Actually Alexander Hamilton and a couple other hard-core Federalists asked the Prince of Prussia to be king, but changed their mind before he could reply.

nope did not happen. but the Confederation Congress did ask I believe the elector of brandenburg (not a Prussian). Hamilton did propose an "elected monarch" to serve for life or removed by impeachment as part of the debates at the constitutional convention hence him being labeled a monarchist, he insisted it was in the interest of full debate and claimed he never voted for the measure himself. Madison's notes were later leaked in the 1790s by James Monroe, who also leaked the Mariah Reynolds affair and these events led to Mr. and Mrs. Hamilton's lifelong hatred of the man. please read Ron Chernow's book on Hamilton, good portrait of the man if a little gentle on his love of business.

But on topic, Monarchy is impossible without Hamilton's idea being adopted, or washington accepting the crown.
 
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