I think Splatterhouse 2-3 where all made by SEGA. The original was an arcade game, while the second was a direct sequel, and the last was an all out aciton ( JRPG, Adventure Island ) game. SEGA benifited from games like Splatterhouse, and created "House Of the Dead" along with the other series, all the way to "Illbleed". That is my hypopothesis, on the subject, of splatterhouse.
It was an arcade, and the PCE was built to do computer games in relation to the NEC series, So it had no problem doing arcade games.
The next idea of why no Splatterhouse 2 + 3 is because like Shin Megami Tensi" it did not sell against the other consoles, so they said, lets just do it on the SEGA, since the SEGA CD was on the horizin.