Because they're just not the same types of abilities, not targetable for single enemy champions or the initial parts of those skills aren't channels. Poppy's is an AoE skill that targets terrain (which actually does go on reduced cooldown if she lets the second part of the ult run out completely, i.e., she doesn't make any swing), Karthus' counts as a global AoE skill (it's kind of unique, but Karthus' ult is easily canceled by external forces and put on full cooldown no matter how it's canceled), and while I have no experience with Fid's ult personally, I know that doesn't make the player target champions, either.
I'm not 100% sure on this, but I believe an exception is made to Vi's ult, which goes on full cooldown even if the target dies, likely because it displaces her as another of its primary effects, and doesn't have a channel. Also, if her target goes untargetable before it can connect, it goes on full cooldown.
In any case, someone like Skarner has the same thing: If their ult starts but doesn't complete the entirety of the channel, however brief (even if Skarner uses one of his ult's quotes), it'll go on a super-reduced cooldown because it didn't complete the channel.