If Hogwarts closes everyone'd end up being home-schooled anyway, so they wouldn't end up with no education at all... but it wouldn't be the same.
I think Slughorn would stay, simply because I think over the course of the year of his return he got addicted to the place again.
Wouldn't it be interesting if it wasn't McGonagall that because Headmistress after all, in due time when the school councellors elected?
Imagine if they voted in Slughorn.. then you'd just have to find a Slytherin head, and a DADA teacher.
And I think you could wrap those roles up with one person, not requiring too many extra stuff.
I'm sure you could find a willing Ministry-approved Slytherin head and auror.
Do we know a good Slytherin to take the role though...?