I also find such "your opponent draws a card" strange… Who wants to give his opponent card advantage? I think you're correct, in a regular game, I will not want to use that response.
I can only imagine that in combination with a milling deck, it can be advantageous to let your opponent draw cards (e.g. with Book of Eibon limiting his hand to 5 but Clover Club Card Room letting him draw to 6; or you would be able to know if a card on top of opponent's deck is a good card via Clover Club Regular and then discard it via milling - or if it is bad, let him draw that card via the Regular).
I've actually tested a milling deck centered on the 'Clover Club Regular'. It also included 'Professor Rice', so my opponent got to draw two cards for every success token for every Regular in play. The milling effect can be huge, but of course your opponent can simply stop going for stories until he's got rid of the Regulars and even if he doesn't stop, he'll soon have almost his complete deck in hand, which usually means he can crush you pretty badly.
Basically you need to combine it with cards that cause the opponent to also have to discard from hand, but none of the existing effects can keep up with the number of cards drawn. The only one that came to my mind is 'Implant Fear', which in combination with 'Snow Graves' discards the complete hand. And if you're using the Hastur faction anyway, another good addition would be 'Cold Spring Glen'.
Regarding 'Premature Detonation', however, I have to agree. It's such a weird card, I cannot think of any situation where I would want to play it. I mean, okay, I suppose there are a few characters with abilities requiring the character to be exhausted that you might want to prevent your opponent from using during the story phase, but cost 3 loyal? For cost 0, maybe, and even then it would be simply too situational, unless you know exactly what deck your opponent is playing.