That's a very interesting question! Yes, that's the most natural way of saying "I'm afraid", but you should rather think of it as an exception, not as a rule - there are very few nouns which can be used that way (Actually, I can recall only "страх", "срам" and "гнус"). It seems to me, it's related to the verbs, these words are usually associated with (i.e. "обзема ме","обвхаща ме"), but that's just a wild guess, I don't know for sure!