Mathematically, it is an interesting piece of work. However, not only will be made more or less obsolete by Schnorr signatures as HeRetiK says, but I have some concerns with it being implemented in practice.

First of all, it still requires trust. It is essentially a 2-of-3 system, meaning the "Service Provider" and "Recovery Server" can collaborate to steal the user's funds. Given that this method does not yet exist, then presumably whichever company first sets it up and offers it to their customers will also be hosting the recovery server, meaning they have complete control over your coins should they turn evil. It also completely relies on this company continuing to operate.

Second of all, even if the "Service Provider" and "Recovery Server" could be spread between two different companies, you are still entirely dependent on this one implementation of the software. If that disappears from wherever it will eventually be hosted, could you recreate it and recovery your coins? Again, it involves a lot of trust.