My guess is that in the village, they have a safe supply of blood. If he drank from randos while traveling, OTOH, he'd attract the attention of vampire hunters and die.
They don't patrol everything by themselves. They lead monster hunters. (And there are other Stewarts - cousins and uncles.)
Are the central nobles short sighted? Yes, but sometimes that's life. And it wasn't so bad when the barrier was stronger. But they haven't had a magician for ~100 years...
That area of the world building is questionable, yes.
That said: they're called borders, but what's on the other side is monster land, not another country. So being a lord there is about dealing with monsters, not foreign relations.
The Stewarts are a family of meatheads. Even the scholar...
Called the murderer in the first chapter:
https://forums.mangadex.org/threads/detective-conan-ch-1160-escape-from-the-mansion-of-twelve-zodiac-signs.2611602/post-29642349
But not the motive.
It's the sommelier. The victim discovered... something. Maybe the sommelier lost his sense of taste or whatever. He covered it up with his "prank", and then blackmailed him. But of course the blackmail victim struck first.