The "Merciless Catalyst" dropped for me! Here is how it happened: I very, very, very rarely play Nightfall Strikes (I play normal Strikes a lot), but now at the end of the season I had nothing else to do, and I decided to do Strike-Bounties. So I did 3 Nightfall Strikes with my 3 Characters each. And with my third Character the Catalyst dropped off of an enemy! So after 7 or 8 Nightfall Strikes back to back it dropped! And I read somewhere on Reddit, that some Bungie-Dev said, that the Droprate is greater on stronger Opponents.

Nope definitely don’t need it equipped that’s for sure, it’s just their crappy RNG system.

do not need to have it equipped. i just had jade rabbit catalyst drop after months of crucible hell and now it's even worse because i have to use jade rabbit in crucible to finish the catalyst...

As for all Y1 exotic catalysts, their drop rate is extremely low, but they still drop nonetheless. For example, I got the Coldheart exotic catalyst months after getting the original weapon. Y2 and beyond exotic weapons do not have this problem and their respective catalyst will have an almost-guaranteed drop after a core activity completion.