I’d work a museum at 2 A.M. for enough pay and time off.

What's your problem? It's not like employees are doing it for free.

So night guards shouldn't exist?

They are. But it’s a rhetorical question anyway. You will always find people willing to work at any time if you offer them enough money or if they are desperate enough.

to add to the neighbour comment: Night shifts are very popular in German car factories as they give good money.