In Season 6, we find out the following about the magical properties of the wall:
BENJEN: This is where I leave you.
BRAN: You're not coming with us?
BENJEN: The Wall is not just ice and stone. Ancient spells were carved into its foundations. Strong magic to protect men from what lies beyond. And while it stands, the dead cannot pass. I cannot pass.
—"Winds of Winter" (Game of Thrones, S06E10)
So why would the men of Westeros need to worry about the Night King and his army? Couldn't they sit back and enjoy the wall's protection?