I won't pretend to know what Jon will do, but I find it extremely hypocritical that folks are holding a political decree over the safety of the free world. Especially since being an independent kingdom is something no one was ever clamoring for before the Greatjohn Umber (I mistakenly called him a Karstark before) opened his big mouth (really just sucking up at that point after Robb already had to put him in his place). The Mad King wild'd out, so they overthrew him, they didn't secede. And that was during peace time where they weren't worried about a greater battle. So why is simply overthrowing the Mad Queen not enough now? Now, when they need be focused on the real threat?
And she's not just sitting on dragonglass, she has an army and 3 dragons...
Well....you gotta look at it from the North's point of view.
The North follows the Old Gods....the South follows the Faith of the Seven.
IRL, this is like Christians and Muslims sharing a country. There's a huge culture divide off that alone.
The North bent the knee because Aegon came through with 3 big ass dragons but, really nothing changed for them. Aegon allowed The North (and Dorne) to essentially be quasi-Kings. Lords from the North almost never came down to the South. For example, the Lannisters, people from the Reach, the Riverlands and the Stormlands were much, much, much more involved in King's Landing. Even, the Dornish eventually got back involved in King's Landing after they married into the royal family. But The North however, with the exemption of Cregan Stark, almost NEVER went down south.
So the North asked themselves why on Earth were they a part of the Seven Kingdoms when they shared nothing in common. Oh yea, them big ass Dragons.
But eventually the Dragons died off and there was nothing keeping the North from seceding because without Dragons, the South cannot take the North with a regular army. But since they had been in the Seven Kingdoms for 300 years, they just stayed because they had been in it for so long.
Then.....Aerys the Mad King boiled their ruler alive....Ned's father (Southern Ambitions though!). And then killed the North's heir, Ned's older brother.
So while the North was still wondering why they were still fukking with these nikkas....the South did them mad flagrant by killing Rickard and Brandon
But alas, Ned and Robert killed the Mad King. The Rebellion was successful....their deaths were avenged....all was forgiven and things went back to normal.
The Starks went back to the North to their own peaceful lives again. Staying in the Kingdom but, not fukking with the South.
Except 20 years later, Ned, the next Lord of Winterfell got killed by them too
Plus Robb
And Catelyn too
So from the North's perspective, the South has killed
four of their leaders within 20 years (Rickard, Brandon, Ned, Robb), they have no connection to the South having a different culture & religion and without Dragons keeping the Starks/North in line, there's nothing the South can do to keep the North from seceding.
Jon needs the Dragonglass. He'll probably need Daenerys' dragons too. But that's gonna be a tough sell getting the North to ever go back to the 7 Kingdoms. I personally don't see Dany or her dragons making it out the war. She's a Conqueror. Not a Ruler. Dany and her dragons will die helping to save Westeros from the White Walkers.