So, by slappin' letters & maintainin' the number registry for the Enterprise was a PR move. The Enterprise was also sent on unusual diplomatic missions & brought into action for galactic changin' events.
Thus, the flagship of the Federation.
Exactly. Look at the "launch" of the completely unprepared Enterprise-B; it screams of press junket. Probably penned-in months in advance, and they rushed to get the ship space-worthy to meet the deadline. It was, after all, only a "quick run around the block".