It was a huge oversight by the showrunners to act as if the wall and the night watch were still necessary even though there were now zero threats in the north due to the destruction of the white walker army and the Wildlings now being on friendly terms with the Seven Kingdoms.
Finally saw last episode last night. More thoughts later.
To your point, however, I don't think the white walkers ever die, as they walked thousands of years earlier and were defeated by dragon glass as well. I feel the writers did a poor job closing this loop and explaining this to the audience in the end--and my theory is they will return, yet again, when the King of the Night is reborn, and I think he is just as tied to the history of Westeros as Bran is, likely intertwined with the same source as Bran encountered when he went north. Like the seed from a sapling. One incarnation dead, another will be reborn.
The only question is, if this is so, why is Bran not aware of this, as he seemingly knows everything.