Thing is if the united states where to join the commonwealth it would have to accept a monarch having some modicum of influence directly on the Us, due to Lizzie's position as head of the commonwealth, which as far as I remember is not what the great majority of Americans want.
I may be wrong, but the Queen has almost no real influence over the Commonwealth. Seems that would be Kamalesh Sharma, the Secretary General of the Commonwealth. Mr. Sharma is an Indian, a republic that has no legal role for the Monarch, and a nation with its own troubled break away from the mother country.Consulting the source of all knowledge, Wikipedia, it looks like of the Commonwealth members, 17 have the Monarch as head of state, and 16 are Republics like the USA.So I don't see the Commonwealth as a return to Empire, but as a common cultural exchange organization, like other organizations the USA belongs to. I guess all I'm saying is that the more the US can do to increase common cultural exchanges with like nations, the better.