And while it may be low energy to run, creating hard drives just to prove you have space seems a less than environmentally friendly activity.
It looks just like another proof of waste
Storing the whole chain takes a bunch of space anyway, so you have a similar storage problem there too.
If you want to see how cheap persistent storage can get, look up the cost of Amazon Glacier. It's shockingly cheap - $0.005 per GB or even less.
GPUs or ASICs for hashing are going to have a limited life span just like your storage hardware, too.
In PoW you can lower your environmental impact by using clean electricity. For Proof of storage it would be 100% manufacturing.
The probability of being awarded a transaction is proportional to your reserved space 'plot' compared to the globally reserved space. Assuming it takes off, and enough 'overprovisioned' storage has been added to the pool, then it makes little sense to buy hardware just to farm storage-coins. The tiny increase in probability just wouldn't pay off.
The main cost of hard drives is intellectual property (ie. Paying for the R&D, patents and licenses for all the tech inside).
It isn't clear that "wasting" intellectual property is in any way bad for the wider economy. In fact, it probably just subsidies storage for the rest of us in the long term.
Instead of electricity consumption the limiting factor will be raw materials to manufacture storage. Likely even worse for the environment given the energy and raw material cost to manufacture storage devices.
Just like PoW it makes sense to spend enough until a breakeven point. In thise case there is a direct incentive to buy as much storage as possible.
And nobody cares. If I had to guess, I'd say the attractiveness of mining the PoW coins is that it's very expensive, but accordingly very rewarding.
When the coins are cheap and easy to secure as a node, people seem to not be as interested, which means the coin doesn't get used.
Chia, Sia, Filecoin all are trying to do similar, but have added in a "distributed Dropbox". There are some interesting challenges there, like quintuple redundancy and having your files stored across multiple nodes in shards for privacy. But in the end, they seem to suffer from the same issue as BURST: their feature set struggles to create popularity because they're not Bitcoin.
If they did that, they'd get over the "we're not bitcoin" hurdle, assuming the tech was any good.
That way there is no proliferation of coins, and people will have trust knowing each of your altcoins is backed 1:1 with bitcoin.
You set up a system, which inherently ensures a certain resource will remain/become scarce (...for all of humanity), or fail. That's just super counter-productive for human prosperity...
It uses "Proof of Space" (proof that you're allocating a certain amount of storage space) instead of Proof of Work or Proof of Stake. Pretty interesting and they're coming out of beta into their mainnet in the next few weeks. Their on-chain programming language is even Lisp-based!