You almost convince me on a part of your argument. The reason for so few Centaurs, Ambassadors and others might be that they were not allowed to build that many.
But that begs the question, why do they have so many of them to start with?
Even disregarding my theory entirely, it might just... not work, or just be ridiculously difficult to make work.
To clarify, I could see the Curry as having a story like this:
It started out as something like the Centaur but scaled to the size of the Excelsior-class, like the Centaur is depicted in video games. It was later taken out of active military style service, and may or not have received engine changes, and then probably became a cargo ship, still used in war, just now for supplies not fighting.
While I think the above is possible, I do not believe that the Curry, or the other ships, actually come from searching interstellar "battlefields" for parts. I do not see it having a story of Starfleet seeing an Excelsior-class hull in 2 pieces, and a Constitution-class pair of nacelles, and then somehow thinking that they could assemble all four parts into some new and very unusual configuration, and have that work safely with warp-drive physics.
I do think Starfleet could have "developed" this design for a freighter after studying and using new-but-unused or decommissioned parts. A ship from spare parts, not random parts that survived a fight.
The "saucer over the aft part of the secondary hull" configuration must be original to the ship: despite the secondary hull sticking out forward of the saucer, it just too closely resembles the shape of a Ptolemy with a cargo pod for me believe that it was originally an Excelsior-class that or some reason was more viable to be repaired with the dorsal at the back instead of the front where the dorsal was designed to go.
If warp nacelles were self-contained engine pods as regular nacelles can be, then I could see the TMP style nacelles being added to a new designed hull later. Since there is a warp core and a reaction chamber inside the hull, then the tech is almost certainly too complicated for Starfleet to be able to just "bolt-on" new engines from an older, different design. The Curry and other ships like it would have to be "designed" or "redesigned" to accept these nacelles, and I don't see that as a process they could figure out whenever a battle was over to use whatever was left.
With newer nacelles, they could have been designed to fit older ships also, but there is little evidence for that. The Freedom and Niagara look like they could be older and have once had older nacelles. The Enterprise may have gotten new nacelles for TMP..
Even so, what other “escort” type ships have we seen in Trek?
Potentially the Miranda and Centaur are the escort ships of their eras. I was going to say that if this is what escort ships look like in Star Trek, it could explain why the Nebula-class Phoenix is so powerful in its episode, although the stealth may have something to do with its special pod. The Yeager from DS9 might be an escort, too. Maybe the nacelles being below the hull help indicate this. The Elkins could be an escort, too, but again, there is the issue of the TMP era nacelles that would work better if replaced with the same size nacelles but of a bit different design.