And in the episode with Worf's adopted brother.
That was the TOS Prime Drective.
OK, maybe I shouldn't have said "plenty," but that's at least two, and it's a monstrous enough policy. We can also assume it happens more frequently, but how many episodes of "the crew stands by and does nothing while millions die in natural disasters" could Trek and the audience have taken?
I was also lumping "dear doctor" in with this, but that's not quite fair since that was Archer acting on his own before a PD or the UFP. Though I'm sure Picard would've made some b.s. speech applauding Archer's decision had he been there.
In "Homeward" it would have taken thousands of starships working around the clock to evacuate that planet, thousands of starships pulled away from their other equally important duties that are now unfulfilled.
They would then have to find a new world for them to inhabit, make sure that the world is uninhabited and nothing in the ecosystem will kill them. A huge support team would have to be left there for years to make sure that they all adapt to this and somehow get through with their culture intact (likely impossible). The Feds now have a new pet vassal state that once was a thriving independent culture. Bravo.
Also, in a larger geopolitical sense saving this one world like thay would set a new precedent in that it's what Starfleet MUST do in all such situations from now on and there must be a Task Force to deal with it.
In order to create this new task force personnel and ships must be pulled away from other duties like, say, DEFENSE and put to work, thus ultimately weakening the Federation in an obvious way that their enemies would clearly notice and capitalize on.
Congratulations, you have turned the Federation into a Galactic Nanny State, created various dependent Vassals who can't survive on their own, and given signs to your enemies that you've weakened yourselves and your economy leaving your territory or contest regions ripe for the picking.
Nice try, but when we see the PD invoked in modern Trek, it's invoked for ideological reasons, out of a belief in non-inteference, NOT out of a fear of the logistical difficulties that interference would bring.
Besides, don't forget that cultures they help are also potential new allies, just like in the real world, when countries that get humanitarian aid from another country tend to view that country more favorably. Even from a realpolitik standpoint it makes sense.