For the file storage people, there's a bunch of startups (like Storj and SIA) that have an S3-like API but slice up the files and store the (encrypted) chunks on the disks of "miners" who get paid each month for disk space and bandwidth used. Because most were started during the ICO boom they all use a blockchain token, even though there are usually centralized servers keeping track of which client uploaded which file. The clients could pay normal currency to those servers, who could distribute it amongst the miners.
I used to have a spare PC with a 13TB HDD mining Storj for a couple of years and it worked fine, but converting the tokens to currency I could use was a major hassle.
S3 has quite a significant markup over the HW and electricity costs. Sometimes up to 10x, you can see this by how much discount percentages sales reps are willing to apply to cost of storage. Many of these smaller providers charge a smaller markup and are thus cheaper than (non-discounted) S3.
Cheaper storage alone is enough to lure some people away. There are also people that simply hate AWS for reasons of their own and choose a startup provider for ideological reasons. Finally there is the obvious application of encrypted storage, to store material that is illegal in your jurisdiction.
Similar to IPFS or Freebase, these censorship-resistant distributed storage solutions can help oppressed journalists in third-world countries get the stories of their oppression out.
I used to have a spare PC with a 13TB HDD mining Storj for a couple of years and it worked fine, but converting the tokens to currency I could use was a major hassle.