but I can't think of any tasks in my life so cognitively exhausting relative to their mundanity that it would make sense to outsource them to India.
I think part of OP's point is that you don't realize how much relief you will feel about outsourcing the task until you actually do the outsourcing.
I don't think that is the OP's point (though OP is welcome to correct me on this). If it is, it's highly implicit in the original comment. It is a worthwhile point to mention, though. The difficulty with these tasks seems to be identifying them, rather than solving or managing them.
There's a lot of background mess in our mental pictures of the world. We try and be accurate on important issues, but a whole lot of the less important stuff we pick up from the media, the movies, and random impressions. And once these impressions are in our mental pictures, they just don't go away - until we find a fact that causes us to say "huh", and reassess.
Here are three facts that have caused that "huh" in me, recently, and completely rearranged minor parts of my mental map. I'm sharing them here, because that experience is a valuable one.