I've been lucky enough to have caught about 5 emperor butterflies, but for me the koi is definitely elusive (I only have 2).. I think it also depends on where you constantly go to fish/find bugs? I find that I tend to go to ocean for fishing in pocket camp, more than the river. It's also because the fish size is close enough to a common fish that you've probably walked right by it or scared it without knowing.
Maybe if you keep trying, you'll catch more? I'm not sure to how the logistics work, since day of time/season doesn't affect, it's purely based on luck.