I understand the difference between -pu' and -ta', but I don't understand why one might choose to use one over the other. For example, in this sentence, it seems almost redundant to use -ta', since I can't imagine qop happening, if not intentionally. Since -pu' does not preclude the action being intentional, why would I ever want or need to use -ta'?
-ta' is more expressive, since it has a narrower meaning. Speaking a language isn't just an exercise in logic; it's about expressiveness.
The same might be said of the difference between -taH continuous and -lI' progress, since you can use -taH even if you're making progress toward an endpoint. At qep'a' wejDIch a group of people were playing a name-that-tune sort of game, and it had been going on a really long time. I stuck my head in the door and said, SubomlI'be'; SubomtaHqu'! That got a laugh. It also shows how these suffixes might be used differently.