Make remove curse first require that you identify a curse for removal. One way you could do this, is give remove curse a radial menu that removes a specific curse (so you select Remove Curse of Urfestra for example); maybe there is another way to do this too. Instead of someone just hitting remove curse and it removing all their curses (bypassing the need to detect).
Additionally, make detect give a +2 to all remove attempts for curses that you detect. So if you detect Curse of Urfestra then you use Remove Curse of Urfestra, you get a +2 to removing it on that subject.
Basically right now, to handle curses you just need to wack remove curse at someone and boom: all removed (plus you can meta-see which curses you attempted to remove iirc).
What I think would be more interesting, is for Detect to first be used to diagnose and then Remove used to remove the specific curse. Remove should also not tell you what curses you tried to remove.
If you wanted to ramp it up a bit, you could make removing the wrong curse cause a surge in the subject. Or you could keep it so if you want to remove without detecting, you need to play wack-a-mole. I think the former would be more interesting, but that's just my opinion.