Pinhead is kind of a bitch

To be fair, it became clear after Frank stabbed Julia that he didn't give a crap about her, since he began draining the life out of her while saying "nothing personal, babe". I don't think he was all that interested in Julia, and used her love/lust for him as a means to an end. And I think he was also more interested in Kirsty by that point, so who knows, maybe he missed on purpose.

The cenobites coming after Kirsty while she banishes them back to Hell with the box may have been a last-minute idea, to bring it more in line with typical 80s horror/slasher flicks. Still, a later movie may explain why the cenobites did so little to stop her. In Hellraiser III, one of the characters states that Pinhead can't take the box, that it must be given to him. Another thing to point out is the production had pretty much run out of money by the time they filmed the climax, which probably affected the special effects of the cenobites being sent back to Hell, as well as house collapsing.

I think the problem with people complaining about Pinhead being defeated in Hellbound is that Pinhead isn't really like those other horror icons. We're not here to root for a killer who mows down scores of horny teenagers. The story comes first, and in this case, the story called for the original cenobites to die. Also, if you'll remember, a lot of those other icons were defeated by human teenagers and children, while Pinhead was defeated by a much more powerful cenobite with a direct connection to Leviathan. So how is Pinhead a pushover when he's defeated by another cenobite who was granted with greater powers and has the ability to turn other cenobites back into powerless humans, while Michael was blown up by a middle aged doctor and an injured and sedated teenager, and Jason was hacked to death by a small boy?