Unlimited data storage reduces the utility of Bitcoin as currency. I just had to upgrade my bitcoin drive from 1T to 2T. Use another block chain for arbitrary data and store hashes, with actual data using a distributed storage protocol like IPFS. Note that if you want reliable storage, you will have to pay for it (with BTC). But volunteers will have fun hosting data - until they need a second job or whatever.

One problem with volunteer data storage (including on Bitcoin) is illegal images/files. One solution I've been considering for IPFS is encrypting files using the hash as key. So you have to know the hash to get the file.
BUT, if the feds raid your house, and the database/filesystem can iterate over all the hashes stored (as is the case with normal hash/btree/etc indexing), then they can search for illegal images. And if there is one (there is - that is how they got a warrant), off to jail you go (unless you have corporate lawyers to insist that you are a common carrier with no control over what files are stored).
I've had several ideas for a non-iterable filesystem - but it is a tricky problem. And might not solve the problem, and LE will just poll all volunteer servers to see who is storing an illegal hash.

Another solution is a govt database of hashes for illegal files (i.e. blacklist). But that entails it's own censorship issues. And actual criminals can change just one pixel or add an extra letter to a classified document to change the hash. So the law enforcement value is not that great.