Yeah, I’ve heard that theory for many years, and it doesn’t quite fly for me. If the reason why we saw so few Ambassadors was because they were all away on deep space missions, then why didn’t we see any more Sovereign, Norway, New Orleans, Challenger, Springfield, Cheyenne, Freedom and Niagara classes, and the Centaur, Curry, Raging Queen and Yeager types, not to mention the 15 or so conjectural classes mentioned in the Encyclopedia, all of which were seen on screen even less, or not at all? Were they all away on deep space missions too?
The only real on-screen gauge we have to determine the bulk of Starfleet’s active duty ship classes as of the 2360’s-‘70’s are the DS9 fleet scenes. And those ships are only composed of primarily Excelsiors, Mirandas, Sabers, Steamrunners and Akiras with a smattering of Galaxies, Nebulas and Defiants. The latter three can be chalked up to their relative newness of the time period, which leaves an extremely odd combination of two extremely old classes mixed with three relatively newer classes.
But I digress. For the matter of the Ambassador, my head canon is that the class simply wasn’t all that popular and was phased out early. There weren’t even other ship classes which utilized its parts, unlike the Constitution, Excelsior and Galaxy classes. It was just a fluke that one of those ships happened to be given the Enterprise name and registry. It’s not an elegant theory, or even one that I particularly like, as I like the Ambassador class design. It’s just that in the absence of other evidence, what’s left leads me to logically assume the class didn’t live up to expectations, and not a lot of them were produced. This would explain why most of the ships (and the other above classes I mentioned) have registry numbers that are very close together, rather than the more spread out numbers of the Excelsior and Miranda classes, which seem to have proliferated more over the decades.