I can do something reminiscent of "m of n" control tools, FEC or striping algorithms, but now the client is doing multiple fetches and matrix multiplication on every single request.

If I'm just trying to make sure there are 3 copies of my home page on IPFS, then I need 3 copies of the same file in three locations. And those locations all need to be online when I want to challenge them.

The Bitcoin protocol is designed around low availability of individual nodes and inference of consensus. Any 'proof' has to be uploaded while you're connected. Uploading a proof (of work, stake, whatever) to the network proves you did something, there is no need to challenge that fact, and you can disappear for hours or forever. No voting, no challenges.

Proof of storage requires challenges, which requires availability (well, storage also requires availability, otherwise what's the point?). If you insist that almost everyone is online, then you open the door to other consensus algorithms. Ones that can, for instance, handle non-repudiation.