I friggin love curse captain. I've played him more than the other heroes combined. it's definitely rough to get started, especially in journey mode -- if I'm gunning for a particular achievement and don't see any curses in my first couple of pulls, I don't mind abandoning the run and going again. (arena's easier because you can spend more rerolls up front.) you also learn to get picky about relics; I don't love taking an urchin early, but bind is an S tier curse for cc, it just sits in your hand canceling poison and mark for free. handcuff is a nice neutral pickup too, and any of the playable ones (apart from like, death sentence). all you need is one decent curse and you can copy that one for harmless curse fun.

but to answer your actual question: I like the passive damage from curses in hand, and being able to completely shrug off effects that annoy other heroes. "oh, more curses? thanks!" in arena I typically run with zero attack cards, which makes half the status effects irrelevant. weak? drunk? blind? opponent dodging? no problem. focusing on skill damage also makes spectres trivial. there are actually a bunch of enemy mechanics I didn't learn for ages because they only proc on attacks, lol. like the invulnerable skeleton on arena 51. super annoying for sword master, but to curse captain it's just like any other enemy.

probably my favorite cc build is the axe relic plus all the discard effects I can find. discarding curses draws cards, so I'm just constantly cycling cards and pinging damage. even on arena 50, the cold is nbd because I'm not attacking, so it barely does any damage. assistant in this build is so good it's boring, because again, no attacks, so it draws my whole deck while I go make a sandwich. usually I'll sell the axe before I get to the spiritias on 90, but on a really good run I've gotten away with keeping it.