The logic being that when a culture discovers warp drive, they're more ready for contact, and it's better than having a random confrontation in space.
The logic there is the species now has a warp drive of their own, if you don't contact them, they're going to contact you.
Waiting until they
first form a society that acceptable to you
is no longer an option. Warts and all, here they come.
In "Homeward"'s case, they just needed to go further and explain that it wasn't possible to evacuate the planet in time and that would set a precedent for such actions that would lead to an ineffective Galactic Nanny State.
Homeward is a great example of the lack of conviction Picard has in the Prime Directive. It's easy for Picard to stand aside and simply allow everyone on Boraal II to be killed by a natural disaster, but once he discovered that his holodeck contained a few dozen survivors, by the letter of the Prime Directive shouldn't Picard have turned the ship around and beamed the survivors down to the airless surface. Not doing so was hypocrisy on Picard's part, he's a avocate of the PD, a vocal supporter of it.
Picard didn't want to get his hands bloody.
Just because a humanitarian intervention is doable in one scenario (because of population size, resources, etc.) doesn't mean that the Federation would somehow be forced to intervene throughout the galaxy.
Well of course not, it would be a question of priorities and assets.