I think you'll find this world makes a great deal more sense if you consider it less as a place which arose organically than as a constructed setpiece of some kind.

[There's even background music.]

Just Missy is fine, Miss Granger. I appeared here one day under highly similar circumstances.

And you're completely correct, there is almost always a reason when people are kidnapped across space and time. Unfortunately the actual 'why' of our situation is still a mystery, despite efforts to the contrary.