Why is it when I initially saw Kyon and Itsuki I immediately concluded that this had to be a parody of "Dr. Horrible's Sing-Along Blog"?

The Good , The Raw and the Truant. Love this parody

Not actually a parody, except in broad terms. This is an illustration from the "Haruhi Theater" short stories. The SOS Brigade gets thrown by some agency unknown into a series of roleplaying/fiction scenarios with the same general goals; first a fantasy campaign (see post #269473), then a space adventure (post #266141), and (at the end of the second story) into the Old West. (It probably goes without saying, but they're flung into the second and third settings because they make lots of things blow up and fail to accomplish their assigned goals.)