More efficient than brute forcing a private key, as you would have to do when you don't have the public key.

Sure, finding a private key whose public key's hash is given might be 2x slower, but Pollard's rho algorithm is 2^128 times faster.

Asymptotically, an additional hash at the end doesn't matter when you brute force. But it prevents you from using Pollard's rho algorithm, which does make a difference asymptotically.