While I do want completely new stories too, rehashing old stories makes sense. On one hand, the changes between universes were rarely been dramatic in Star Trek, look at how close the Mirror Universe was to the main universe. On the other, Botany Bay is floating in space, the whale probe is coming towards the Earth, not revising some of them would be a weird choice. Those are big events that are happening in the new timeline, possibly under new and much more interesting circumstances. Why would you pass the opportunity to use them?
I am actually quite content if STID story is what I think it is. It is a new story, telling new events from a new angle, I don't see nothing rehashed. As a revisit, it will only add to what we saw in TOS, adding more depth to the old characters, much like STXI did for me with Uhura, let us explore alternative life histories, give us a peek into Federation dirty business, and show us a lot of brand new things (of my favourite kind, I might add).