The books aren't the greatest examples of Alternate history fiction ever, but I enjoyed them and the premise isn't too implausible. As far as I remember, the reason that it doesn't have serious internal issue due to differing peoples is because the entire area was colonized by people moving west from the east coast. Thus, they all retain a strong sense of national identity. There was also something about the idea of the 'American Dream' - that America is a land of opportunity, where anyone, regardless of social class, can make prosperity for themselves. It isn't true, but it does offer lots of people hope.
And one thing we know from history is that whether something is truth or fiction, if enough people believe in it it gains a power of it's own.
The USNA in the books doesn't sound to implausible to me, simply because considering the massive population and amount of natural resources available from the North American continent, it would easily be a superpower. If it was started by liberal revolutionaries who were more inclined than, say, the Imperial Chinese government, to educate the people, and if these people settled most of north America, you would have a large, well educated population. Combine this with massive resources, and a hint of ideological fervor, and you have a superpower.
I agree, the nation seems lucky. But luck isn't always evenly distributed. And some nations in OTL seem to have been quite lucky since the 1600's, despite having serious disadvantages (Sweden is a good example).
And we must remember that when he says people from their TL would think ours implausible, he is right. Our view of alternate history is constrained by our own comprehension of historical trends, and we only have one data value to work from.
If we could tweak the parameters of the experiment called 'history', and see what resulted, we would get a better picture of how historic trends worked. If we could tweak it a dozen times, our comprehension of history, particularly of certain areas, would be leagues beyond our current comprehension. A graph with just one data value doesn't tell you much about anything