And as it was the prototype of that class, it might have taken a while following constrction to iron out any flaws which appeared during shakedown. Once those had been ironed out and the class entered full production the registry numbers could have gone from where the Consetellation was to where the Enteprise was registry wise.
I think you are confusing "Constellation" with "Constitution."
You know what's cool? When they produced this episode, they never would have thought that we would be dissecting and analyzing the reasoning behind the registry number some 45+ years later.