This is already well known in enterprise storage, and one of the solutions is erasure coding. Some products implementing this exist today and others are currently in the works. Basically you go to something like 20+5, instead of 4+1. Of course this only makes sense when you have 50+ drives in a tray.
Practically yes, erasure coding solutions do tend to have a lot of hard drives. That's probably because their efficiency really makes them much cheaper for people who are buying lots of storage, for a small setup the cost of the drives themselves isn't that significant. But mathematically it works with smaller numbers. You could have an 8 of 12 setup and be able to sustain the loss of 4 drives while only storing an extra 50%.
http://www.networkcomputing.com/storage/what-comes-after-rai...