In the last episode of game of thrones, Sansa asks that the North becomes independent and Bran allows it.
Seeing this, Why didn't the other rulers ask for the same thing?
Especially Dorne and the Iron Islands.
I accept and agree with the answer that was given on SFF (“Sansa was smart enough to wait for everyone to say aye, so they can’t go back on their word”).
However in my opinion there could also be the fact that, the north has always had its own sort of “culture” and independence, there is a certain respect between northern houses. So it’s easier for the other kingdoms to accept them as independent, since they’ve always, culturally, been seen as seperate from the other six kingdoms.
On top of this, the north is the size of the other six kingdoms combined, so having them ruled independently makes much more sense, than in the other kingdoms cases.
It wouldn't make much difference if they did officially seek independence. As a king with little or no family holdings, bannermen, or revenues, Bran would have little power over any of the southern kingdoms of Westeros -- and less ability to influence the North, even if he did reject Sansa's aspirations toward independence. Refusing to acknowledge a king would needlessly provoke a crisis.
The situation is similar to that of the Germanic kings and the later Holy Roman Empire (as well as other European regions) where the monarch was elected from among the peers of the realm. The Emperor would gain little more power than he already possessed, and the electors would have no interest in choosing someone likely to interfere with their own interests, let alone to give the position enough resources that it could be become problematic for them.
In Bran's case, he's now responsible for a devastated city in a region already ravaged by war and overrun with leaderless Dothraki, with no obvious sources of income. No wonder the other lords are happy to leave what's left of the Iron Throne to someone unlikely to bother them while they rebuild their own lands. The Iron Islands won't see the fleetless king as a threat and the Dornish lords in the far south were probably far enough away from winter and the war that they have the troops to fend off any aggressors.
You can see why King Bran is happy to leave it to Tyrion to clean up the mess...