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.
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