I'm willing to play the "suspension of disbelief" game far enough to allow the refit from ST 1-3 to be a completely reconstructed version of the Big E. It isn't entirely without precedent even today - look at the Navy's Iowa-class battleships as originally constructed, as compared to their current look. They have been modified all over the place, including some hull reconstruction.
Starfleet may have simply found it to be cheaper to dismantle and severly rebuild the Constitution-class ships than to start over with a new design, especially if they were in the early planning stages of a whole new class of heavy cruiser, such as the Excelsior-class.
Starfleet may have simply found it to be cheaper to dismantle and severly rebuild the Constitution-class ships than to start over with a new design, especially if they were in the early planning stages of a whole new class of heavy cruiser, such as the Excelsior-class.