It doesn't make a lot of sense IMO to take the saucer section of a Saladin-class ship and make a new Contitution-class vessel out of it.
To convert a Saladin saucer to a Consitution-class would involve a lot more than just plopping it onto a waiting secondary hull, you would have to gut out most (if not all) of the interior of the saucer. It would make much more sense to construct a new saucer.
Well, look at TOS Enterprise vs. TMP Enterprise. As Decker put it "This is an almost entirely new Enterprise." Look at the massive upgrades it had, not just the saucer but the secondary hull and nacelles. What was original? Maybe some of the framework and a few bolts? It would have made more sense just to build a new ship.
I'm guessing that some of the other Constitution class ships also had the same massive re-fit (I doubt the Enterprise-A was a brand new ship considering its short life before being decommissioned.)
I guess different people will create their own in-universe explanation when things don't make sense and there's nothing wrong with that at all!