I think, from what I have read in HoME and elsewhere that Numenor was very much inspired by Atlantis. I am sure I read somewhere that in a very approximate fashion the geography of Middle Earth represented an early version of Europe with the Shire as England, Rohan as the germanic lands and Gondor as Italy, the last stronghold of an ancient empire..... the new lands formed in the west after the changing of the world the "New World " of America......
I guess you can apply the story and it is interesting to do this kind of thing ..... but given his claim to detest allegory (which perhaps doesn't entirely stand up to analysis

) I doubt it was his intention.....but of course intentionally or not a writer is likely to give away a lot of his worldview especially when he writes on such a scale - for example it is possible to find an awful lot of Catholicism seeping through - and if a Brit may dare to say so, there is a lot about America that you can imagine the Prof not being to keen on..........(although he was almost certainly NOT the elderly British academic of urban myth who, when visiting the States, replied to the umpteenth person who told him to "Have a nice day" with "I've made other plans".
However I have to disagree about the loss of faith specific to America - I heard about a report last week that alone of the countries of the fully developed world, the US has increasing numbers of people claiming to adhere to a religious faith. In the UK I think only 10% regularly attend church and soon there will be more devout Muslims than Christians - if we haven't reached that point already..... In the developed world suffering was more inclined to make people lose faith (a category I happen to fall into): in the developing world they found the reverse was true.
Generally I think he would have hated the progress of the Sarumans of the world and their "minds of metal and wheels "...... the pragmatism of global industry ....... ........ And in this modern worlds the Sarumans are more dangerous than Saurons.... easier to unite against an obvious monster .... the sweet talkers whose policies are devoid of any principle other than backing the winning side are trickier..... else why would anyone end up fighting a war against a someone they supported and armed a couple of decades ago...... pipeweed may not be a significant commodity anymore but other things pass through pipes ....or pipelines.......
But I have strayed into areas that have previously caused me to receive unwarranted levels of abuse when I expressed my views on them - so maybe I should leave it there...
And I am a enough of a wooly minded liberal to hope that American BD'ers enjoy their Independence Day ..... as long as they aren't the American who (and I swear this is true) asked this Brit how we celebrate the 4th of July in England......