Robust combiner for preimage resistance
In your construction, if $H_0 = H_1$ (same function), then your $H_{\circ}$ is constant and equal to $0$. More generally, that kind of construction relies on the two underlying hash functions to be "different" from each other in a way which is very hard to define properly, let alone achieve. If $H_0$ and $H_1$ are independent random oracles, then most constructions are fine; but, there again, random oracles don't really exist.