Well, the way I see it, you're partially right. Or more accurately, I think there are more details to consider.
The Night's Watch is an organization that has fallen on hard times because a token force is all that's been needed. Even with the giants north of the wall, which no one believed existed until fairly recently when they attacked, they were sort of minding their own business.
But believing that 'all hands on deck' is the right way to go about it might not really be the answer. If Westeros takes a vested interest in the north, then when the threat is dealt with all of the meddlesome politics will come into play too. Once the rest of the world believes that there is crazy shit up there, how long will it be before everyone wants to use it to their advantage? The Targaryans did it with dragons and conquered all of Westeros with them. The dragons were their trump. And notice when the dragons died out, so did any hope they had of holding on to the throne.
So Westeros isn't the answer. Not unless they change their ways and become more honor bound. The Starks were the best wardens of the North because their simple virtues and honor, while seemingly outdated by most Westerosi standards, are mostly incorruptible. They're not a good fit for the rest of the world, but they're perfect for running things in the North. The Starks were also the most staunch supporters of the Night's Watch and, in fact, it was a Stark that founded the order to begin with. Also, the Starks have the blood of the first men in them and are still observant of the old gods and their ways. They are the only ones that truly understood the North because they were able to exist as a buffer between the North and the rest of Westeros.
And the Lannisters, in a typical political power grab, have fucked all that up. And rather than try to make restitution for Joffrey's colossal fuckup in executing Ned, they fought back and used politics to crush them. This is where their scheming and machinations will come back to bite them in the ass.
Meanwhile the Maesters are preaching knowledge and science and saying that things North of the wall are superstition and fairy tales, and that has taken root in Westeros so much that even the most learned of noblemen, of which Tyrion is representative because all he did was read books, drink and whore, don't believe the myths.
My theory, which has not been borne out by the books and is purely speculation based on all the books and the short stories and the side material that Martin wrote, such as the Worlds of Ice And Fire and so forth:
The Maesters, in their infancy, helped forge the Wall to keep winter (the white walkers) in the North. They enchanted the Wall with magic to be a living thing (as it is in the books) that will not permit the undead to venture beyond the Wall. In the books, it's established that the undead can't go past the Wall as long as it stands. Then they decided to erase all knowledge of the White Walkers and disavow magic in favor of science in the hopes that people would forget about it and carry on. In their minds, as long as the Night's Watch continued to receive support from a strong Westeros, unaware of the truth, then the knowledge and fear that comes with knowing such things would not paralyze Westeros or, worse, cause people to try to exploit it in such a way as to bring about another, oh I don't know,
doom of Valyria. Another Valyria is the real thing the Maesters fear, that magic will be misused and cause another plague to spread for which there is no cure. It's all tied to that, in my opinion.
As long as the Night's Watch was vigilant to fight off the attacks, the White Walkers couldn't damage or destroy the wall, thus opening their path to the rest of Westeros. When the Starks say 'Winter is Coming', it's a warning against the White Walkers,and as they get closer to the Wall the winter grows more harsh. The reason Westeros has such long winters is because the White Walkers have become increasingly difficult to push back. Now, with the Night's Watch being a token force, they don't have enough to stand against them. Also, they've been building their strength for a long time to where even the wildlings are really scared. Shit, even the GIANTS are scared. So they want to get south of the Wall because they know it will keep the White Walkers away from them.
The Boltons are ill equipped to deal with their newfound responsibilities as wardens of the North. They are northmen, true, but they are too mired in the politics of Westeros to respect or realize the gravity of the situation. The Starks are gone. The Night's Watch is a pittance, a mere shadow of their former selves, because of politics and corruption and ages and ages of disregard.
So Jon is doing the only thing he can do: trying to convince the wildlings to fight beside him, unite two lifelong enemies against a bigger threat. And when it's all done, the wildlings will inherit the North, the mystical realm that still worships the old gods and the old ways and a land to which they are well suited to living in. This may not bring the Starks back into power (or it may) but it'll definitely be a sign of the new way.
As for the Starks, I believe that Rickon Stark will eventually rise and become the King in the North.
Sansa will end up with Tyrion. He was very gentle and nice to her, and he'll come to realize that he loves her and she'll realize what a great person he is. And the little guy needs to be happy and deserves a win. This will end the war between the Starks and Lannisters once and for all.
Bran will become the new green man and stay in the north and help guide the wildlings.
Arya will always be a Stark in her heart and she will be reunited with Jon at some point (I think him giving her a sword at the beginning of the show and their emotional separation shows they had a close relationship), but she will be full fledged assassin by that point, living in Westeros and being No One.
Jon will continue to work with the wildlings. With the Night's Watch disbanded, he will no longer have to stay there and:
Oh and fuck the Boltons and the Frays. They will all drown in lakes of blood.
