So...I'm sitting here in Kentucky which has one of the largest underground cave networks in the country. One place near here actually uses a huge cavern for doing data backup storage for business.
Caves have a fairly consistent temperature, are largely unphased by weather above the ground and are still considerably more accessible than the bottom of the ocean. It just seems like a better way to go than sticking millions of dollars of equipment tethered to some data cables and sinking it to the bottom of the sea.