Iam not talking about "competency" but cowardice from the incompetent or common sense of the competent.
Why would a noble who can easily order others to do his dirty work go among the sick and personally, up close, supervise killing of the diseased.
For the same reason they hunt animals up close, despite the risks there.
How many nobles perished in hunting accidents? Or because they were beset by bandits after taking a risky, ill-advised route? There's historical accounts of nobles poisoning themselves in the pursuit of a cure for minor afflictions.
I agree it would be stupid to depict the nobility as incompetent and psychotic across the board, though it'd be realistic for some to be portrayed in such a fashion.
Ultimately it's also a video game so there's an element of suspension of disbelief in the same fashion as with horror movies. You could pick apart any given chase scene in a horror movie, for example, though it's there for entertainment first and foremost so certain elements are played up.