The efficacy of Threaten War appears to be that if you have a core or claim on a non-capital province owned by a country who is sufficiently scared of you, you can get that province, and nothing else, for the price of a five-year truce with that country only and the same AE you'd have got for taking that province in a peace deal.
you can't even loot their treasury while doing so, and its always those small minor countries that seem to accumulate useful stacks of ducats...