The Ambassador might have simply been a ship which isn't all that good, either from the start or due to time; it might have had an extremely limited run, which might have consisted of only 9 or so ships; or they all the remaining Ambassador-class ships were on deep space missions, since at one point in Voyager it is mentioned a ship on a deep space mission has been directed toward Voyager and will rendezvous in ten(?) years (too long to return to the Federation); it might even be a combination of all those things.
I tend to see the Miranda, like the Excelsior, as a multipurpose design that was used for such varied uses as surveying already-charted planets for things like colonization or mining (Reliant), science vessels (Brattain) or a supply ship (Lantree). Most of them would've been pulled away from these duties and sent to join fleets at the start of the war.
I always saw it as the original purpose built combat ship (as far as Starfleet goes), thanks to those big, fore and aft, pylon mounted phaser cannons, and fore and aft torpedo tubes. It has better fire power and coverage than the Constitution class.
There could have been dozens of ambassadors still in service, and we just didn't see any of them on-screen. Logically fleet operations would be concentrated on particular classes to ease maintenance and damage repair requirements.
We see elements of several fleets during the war, but some others (the third fleet that defends Earth for example) is never seen, maybe the second-line fleet's version of "Galaxy wings" are heavy "Ambassador" wings, upgraded like the Excelsiors were and ready to pour fire on any Dominion fleet that approaches.
There's no reason to assume the Ambassador class had any more than nine vessels (at least Memory Alpha lists only up to nine potential ships in the class). If you were writing a story and it involved more Ambassadors it wouldn't be wrong, though.
Post-war, though it might not mean much, when Voyager returns home we see Earth's on call fleet consists of a Nebula class, a couple Defiants, a Galaxy, and a Prometheus.
No, all the downsides of the old ship that I list would still apply even if there had been constant upgrades. Especially with those upgrades, really, as the ship would then be a patchwork of modifications with hidden incompatibilities and the need for six repair crews of modification-specific skills where one originally sufficed.
You are right there are limitations to how far a hull can be upgraded, especially if trying to be economical, however, the whole point of upgrading vehicles or weapon is to eliminate new vulnerabilities, old weaknesses, and extend service life especially without introducing new weaknesses.
In real life, upgrades are carefully researched and engineered, and applied in batches to vehicles currently in use. Each successive upgrade program, be it for a tank, aircraft, or sea craft takes into account all other upgrades and non-upgraded systems to make absolutely sure they work as seamlessly as possible.
Some upgrades are not the kind retroactively applied to old hulls and instead reserved for new builds, but as we have seen in Trek, mid-life upgrades to various classes are a common enough thing. The Enterprise-D was upgraded through the series, as was the USS Lakota (to an extreme degree).