Having only 17 ship types in 100 years doesn't seem too unbelievable to me. After all, that's a whole new class of ship being rolled out, on average, every five or six years. Assuming a service life of only 20 years, that's still a lot of overlap between designs.
At that rate, a ship with a 10** registry might be about 40 years old, which matches the service life we know the Enterprise
had, if we assume it was launched in 2245 and lost in 2283... having a fully refit ship be in service four decades later is hardly unprecedented.