One big advantage would be that you would never have to mow or fertilize grass back there! I had a back yard like that once in suburban D.C. although I think our trees were mostly deciduous. Loved it!
Depending where you are, holly might grow back there too.
And if it's a hot climate, you'll love the air conditioning the shade provides. Lobo ~~~~~~~~~~~~~~~~~~~ Delete the obvious to reply to me personally. ~~~~~~~~~~~~~~~~~~~