Indeed given the miraculous ability of a ship like Voyager to apparently manufacture shuttles ad infinitum...
Nothing miraculous about it, at least no more miraculous than the replicators in the mess hall. If they could replicate food, they could replicate shuttle components just as easily. All you need is the raw materials and the pattern, and a team of engineers to assemble the components, as we were shown outright in "Extreme Risk." Heck, we're on the verge of a very similar technology today with 3D printing.
As for the use of drones in Trek, there have always been far fewer robots depicted in the franchise than there should be. Why don't they send down robot probes to survey new planets before risking a landing party? Where are the maintenance robots that keep the ship clean and perform repairs in hazardous environments? We don't even see Starfleet crews using waldos to manipulate mysterious alien technologies within quarantine chambers -- they just work with them by hand, usually right next to the warp core.