Aside from saving actors, I think it's the concept of the two royal couples supposedly mirroring each other.

Speaking of mirroring: when I was at the university, one of my professors had us write a paper of compare and contrast of Midsummer Night's Dream and The Tempest, specifically Oberon versus Prospero, Puck versus Ariel, and how the whole thing worked as a theatre metaphor (i.e. both Oberon/Puck and Prospero/Ariel making other characters act out plays of their devices).