There's potential there. You only need to store part of the chain and there's an incentive to keep rare blocks.
But the mining is optimized for storing as big of a fraction of the chain as possible, so I worry that the future of it devolves into a few big nodes and everyone else dropping out.
It's possible to fund an immutable data archive using a normal trust. It's possible to verify immutability with traditional hashes. What is blockchain going to add?