My personal theory was that the Constellation was the first ship to be refitted with the new technology that would be later instituted on the Enterprise NCC-1701, the US Navy does something similar called the technology insertion.
While the second ship of the new class was brought forward as the class certification vessel in order for Starfleet to procure more vessels. The Class was ordered for the same mission profile as what early 20th Century light cruisers and sailing frigates, operating alone near borders or contested areas, showing the flag in various alien ports, and as fast couriers for diplomats.
Eventually, the Constellation went through certification trials in order to be formally commissioned. Due to the majority of the class being out on the frontier, the ships were not upgraded nor refitted on a good schedule. A number of the ships were retired due to the resource extensive and time consuming upgrades. The survivors (including the USS Victory which served until at least 2374 from the DS9 okudagrams) were upgraded and had SLEP (Service Life Extension Program) to them.