That seems odd, considering the vehicle replicator in Prodigy is basically that exact thing on a smaller scale.
Exactly.
Given the principles of transporters and replicators in the 24th century, turning drydocks (which are used to build, repair and refit starships) into massive pattern buffers and merging both replication and transporter capabilities should be doable.
There's a thicker section of the drydock at the 'top' usually (most of which can be used to store multiple industrial grade replicators... just line and network them up to occupy most of that space, power them with solar and or/fusion and M/AM (whichever is needed) and start replicating ships into existence.
Problem is that some writers have said they intentionally limited functionality of replicators to just not be capable of replicating whole ships into existence because it makes UFP too powerful (apparently), and that for some reason, you wouldn't really need ships with that kind of capability.
But even if that's the case, again, nothing stops Starfleet/UFP from replicating bits and pieces of ships into existence and assembling them (sort of like prefabrication today).
Transporters onboard a starship can easily beam a shuttle/runabout sized object... just imagine what a networked amount of transporters and industrial grade replicators could do.
Since the vehicle replicator onboard the Protostar can already make a shuttle or various vehicles... scaling up the process to make something like a starship wouldn't exactly be THAT problematic... but again, we can easily just say they can replicate portions of starships and just beam them into place (since starships are supposed to be modular).
Either way, building a starship the size of a Galaxy class (or larger) wouldn't take very long using these methods.
You just establish a forcefield that has the shape/size of a ship you want to create, and star beaming/replicating stuff into it and drop forcefields as sections are created.