The reason William came along this time, apart from Alice's incessant nagging, was also because of several "Chosen Ones" in this area.
Yesterday, he didn't rush to eliminate everyone completely.
Such matters, of course, are more interesting when done slowly.
If things go as expected, the ultimate mission of these "Chosen Ones" is to kill William.
However, it's certain they won't be able to do it, as the real goal of the person behind this is to have William kill them himself.
When William kills, it also strengthens the power of that thing,that seems to be its real purpose.
Also, anyone close to William who encounters misfortune, increasing William's negative emotions, would also strengthen the power of that thing. That's why David's mission was to forcibly have sexual relations with Lila.