That also works with the quite low hull number of Grissom. I would posit that the Oberth's were in the first few generation of ships built by the Federation Starfleet (As opposed to the Earth Starfleet seen in ENT), relying heavily on Vulcan designs. They certainly were quite advanced in their day, but probably are not front-line hulls by even TOS, let alone TSFS. If the hull frame is sound, I see no reason they wouldn't go through several generations of refits and modernizations. As Science and Research ships, they won't need the speed and combat performance of the Constitutions, Mirandas, or Excelsiors. Grissom almost certainly is not in her original appearance. The design is apparently a sound one, easy to build and staff, and quite reliable as well. I would dare say the Oberth's are the most successful design in Starfleet, surviving from the early 600 registries through the 60000 registries (spanning at least a century and a half, if not more).
Real-world equivalents: some Royal Navy sailing ships from the days of the Spanish Armada (late 1500s) were still in service in the late 1800s - though when Jackie Fisher took over, he purged them very quickly, and brought about the Dreadnought revolution). A couple of Liberty ships and some ocean liners from pre-1945 are still in use today (though there are few). Many ship designs post 1945 are fundamentally the same as the mass produced liberty and victory ships.