I don't get it. Even with a very fast home connection, it's still going to be faster to use a local hard drive than download/upload from/to a VPS somewhere. Also, hard drives are a one-time cost rather than perpetually paying for your VPS. And if the sVPS provider dies, then what? You'll have to download all your data (see point #1, above - slow) and find another one and upload it all again (or, best-case scenario, you find another provider before provider #1 deadpools and use wget to transfer everything, still a pain). With a 1TB hard drive sitting next to you, it's not going to deadpool.
Possible advantages:
Offsite backup - Okay, maybe, but I would only keep a few of my most critical files backed up offsite, which wouldn't take a huge sVPS. Or, get another HDD and keep it at your friend's house. Or have just one and keep it in a firebox. Offsite is overrated for personal data IMHO.
Cheaper in the short run - I guess it is cheaper to pay for a storage VPS for say, $5 monthly than to get a big hard drive. But let's face it - aside from it being more expensive in the long run, you're also getting less storage, and you could probably dig some HDD out from some old machine somewhere to back up things. Heck, I have a stack of them sitting around.
But that's just my opinion. Maybe someone else can help me figure out what the draw is who uses one.