Bandgap of a semiconductor for photocatalytic water splitting
The original purported advantage of semiconductor|liquid junctions proposed by those in the field of photoelectrochemistry arose from the hypothesis that charge carriers would have a shorter distance to travel than in solid-state photovoltaic systems, thereby allowing lower quality materials to be used in an integrated solar energy system and still achieve high conversion efficiencies. In theory, one would also be able to avoid forming metallurgical junctions, say those p-n junctions made by using different dopants and creating a well-defined interface to separate charge carriers. Instead of forming these solid-state structures, you can define the electric field by selecting a suitable redox couple in solution. The specific energetics of the semiconductor and redox couple will then define the maximum power obtainable from the given system, so this is why the valence band must be below the energy of the OER and the conduction band above the energy level corresponding to the HER. By natural induction, this means that the bandgap must meet or exceed 1.23 eV, but this is only a thermodynamic constraint.

In reality your system’s bandgap must actually exceed 2.0 eV, this is due to the kinetic constraints based in part on the OER (and to a lesser extent the HER ) and losses encountered within the light absorber. Of course, for a single light absorber there is a tradeoff between the percentage of utilized solar flux and the bandgap. 

This explains why many efforts are focused on using dual light absorbers, with one dedicated to the anode and another for the cathode. In this tandem structure they can efficiently utilize more of the solar spectrum. If you were to stack these light absorbers and use a 1.2 eV and 1.8 eV materials (with each one carrying out one of the two half-reactions required to split water), you could in theory get twice the efficiency compared to a single absorber with a bandgap of 2.2 eV.

Now are these semiconductor|liquid junctions going to beat a dedicated photovoltaic solar panel/electrolyzer any time soon? Maybe, but probably not. Is water splitting really worth doing? Maybe, but probably not. Is it a beautiful idea? Definitely.