The problems with the scheme you presented aside, you've misunderstood the problem. The goal isn't just to be able to do limited things like searching or other

The problems with the scheme you presented aside, you've misunderstood the problem. The goal isn't just to be able to do limited things like searching or other select things, the goal of a fully homomorphic cryptosystem is to allow any computation on encrypted data. Existing relatively feasible partially homomorphic schemes exist that allow you to do some things on encrypted data, like adds for instance. Search is also possible, I think. But neither have much to do with whether a fully homomorphic scheme is practical.