I don't see any particular reason not to, if the kitbashing is justified in-universe. Maybe AutoCAD 2340 will finally offer powerful enough design tools for Kuznetsova to make a hospital Galaxy variant in an afternoon.
The problem is that if we have fifty ship classes or however many, we
also have an enormous array of different kinds of parts, maintenance requirements, and performance characteristics. Furthermore, many of those classes will be almost indistinguishable from each other in terms of actual performance, representing
at best different solutions to the same problem.
That isn't a good idea in real life. There are a lot of advantages to mass production, and very few advantages to having your entire force consist of hand-built prototypes for classes you aren't prepared to commit
for mass production.
Even if we could design ships by snapping our fingers, that doesn't mean we would want to have a huge number of closely similar designs, as opposed to a single consensus design.
Event DCs creeping up is irrelevant. If it happens, it'll happen because both generalist and specialist ships are getting better.
Harder event DCs punish a generalist ship with low overall stats much more harshly than they punish a specialist ship. An
Oberth is still competitive at the one thing it even tries to do- science, because its specialist stat is so good that it can accomplish that particular mission even as the mission gets more difficult. In the context of being a 2260-era ship, it was admirably "future-proofed" in its intended mission. That future-proofing is only now starting to wear off, fifty years later, and in canon the ships were still doing their job fifty years after
our time.
By contrast, an escort with 'balanced' stats but comparable
total stat values (say, 2/2/1/1/2/2) would be an utter dog of a ship that we'd be desperate to get rid of. The
Mirandas, for instance, are actually close to being this bad. And if it weren't for the potential to upgrade their durability to make them into solid combat escorts, we'd be seriously considering retiring them so we could put the crews into more capable ships. Just like we did with the
Soyuzes.
Also, you have to ask what the alternate world looks like. Specialists have a lower failure rate, but that's partially because they simply don't show up to some events that a generalist would. Is it better for a ship to show up at 12 events and succeed at 9, or to show up at 9 events and succeed at 8? There's less of of a chance of a bad outcome from a failures, but probably fewer successes overall.
The trick is that every time one of our ships shows up to the 'wrong' event and gets blown to
Fiddlers' Green, we lose the potential to have that ship show up to
future events.