Probably a hold-over from UESPA - United Earth Space Probe Agency. When the United
Federation of Planets was formed, they likely preserved the "U" for that very reason.
As for the NCC - BK613 gave a good point that honestly never occurred to me in the almost 40 years I've been watching Star Trek. "U.S.S." has periods, implying an abbreviation. "NCC" does not.
Holy shit...something just occurred to me...in TOS, have we ever seen anything other than Connies with a registry number? Could not the "CC" in NCC stand for "Constitution Class"? What if the USS Reliant should have been "NMC-1864" for "Miranda Class"? I know that was before "Miranda" was ever assigned as a class name (a name which I never liked to begin with), but is it possible that the letters in the registry could indicate the class name? It's likely an interesting coincidence, but still...