I wonder if Larian had to "rush" the game out and hadn't quite finished all of the Karlach story paths?? Maybe that's why you walk past so many options that technically should be exactly what she needs to fix her heart, but the game simply ignores them. You have no dialog options with anyone to continue her quest.
If this isn't a case of Larian not quite finishing a character storyline, then it looks like they were willing to create gaping plot holes in order to deliver a tragic story. Not good writing. Plus, it's quite emotionally manipulative to be sure to take the sunniest, most enjoyable character on the team and off them, just because...
Based on some of the news, and some things Karlach's (stellar, wonderful) voice actress mentioned, it seemed that a lot of work on her came in the final year/months of development. So that is certainly a possibility.
I'm going to hope that's all that's going on here. Plot holes and obvious leads left unfollowed only because her story wasn't finished yet. So maybe there will be an update eventually that finishes out other other branches her story could have taken.
I'm nowhere near the end of the game (I'm only 28 hours in), so if the endings in general are abrupt and the epilogues are not there to give us closure, maybe that's what happened there too.