From a behind-the-scenes perspective, it might just be that it had to be that way to match somebody's mouth movements.

From an in-universe perspective, there's probably some reason things developed that way, but Maltz just hasn't gotten around to talking about that particular aspect of Klingon historical linguistics. Maybe it originated as an alternative form of a relative clause, which became restricted to stative verbs. Or perhaps stative verbs started out as English-type adjectives that were attached to nouns, and then they changed over time to be treated like other verbs, but their attachment to nouns remains as a vestige. We don't really know. (It is, however, a lot of fun to hypothesize.)