And I never figured Ambassadors to be created in huge numbers to begin with. I like to think, based on the background, that these ships were the Galaxy-class of their time: the biggest and the best Starfleet could muster, for the big long exploration missions that made us proud. There wouldn't be more than a dozen like her in the fleet, like the Constitution or Galaxy (initially anyway) of their days.
While I suppose that's an ok in-universe explanation, it doesn't really fit with what we saw on screen.
Ent-C: Operating near the Klingon border in 2344.
Zhukov: Rendezvousing with the Ent-D to transfer a Vulcan ambassador.
Excalibur: Assigned to the tachyon detection grid.
Yamaguchi: Participated in the Wolf 359 battle.
None of these missions I would classify as "deep-space," nor would I infer that the class was made for deep-space exploration based solely on this.
And while your point was that all the "other" Ambassadors with these four exceptions were all away on deep-space missions, simply because we never saw much of them, then how do we explain the absence of the numerous other classes we only saw a few times or not at all?
Where were all they during the DS9 fleet battles against the Dominion? Deep space as well?