The reason the flag at Fort Sumter had only 33 stars when there were 34 states is simple. The law (4 USC 2, for the curious) says that the star is added to the flag on the 4th of July after the state’s admission. The 34th state (Kansas) was admitted in January of 1861, and the fort was attacked in April.
Actually, I don’t know that that law was in existence at the time. Lincoln stopped in Philadelphia on his way to his March 4 inauguration, I remember, and took part in a ceremony at Independence Hall at which a new 34-star flag was unveiled. Maybe they were getting a jump on the actual formal admission of Kansas, or maybe the garrison at Ft. Sumter just hadn’t gotten around to sewing another star to their flag. They did have some other things on their minds around then, as I recall…
The code section in question was added as of July 30, 1947, according to this web site.. Whether or not there was a similar prior code section, I do not know.
I think it is more likely that the next US configuration would consist of 52, rather than 51, states — even if the admitted entity had to be broken in half first. There is no way that one of the bipartisan monopoly holders on government would allow the other to add an extra state to the electoral college.
I tend to agree that politics will make addition of states difficult, for much the same reason that addition of representatives to the House is probably out of the question.
There is also the factor that they wouldn’t have thrown out an otherwise perfectly good flag just because the number of stars was suddenly incorrect. While ceremonially important flags, such as the one on the Capitol, would be changed at once, the normal practice for “everyday” flags is to put the new one up when the old one is worn out. This is frequently addressed specifically in such changes, where the government directive says something along the lines of “change will occur effective XX date or at such time as existing stocks have been used up”.