That's not really true in all dialects of English. In my midwestern US English I frequently say that I have a surgery scheduled for Friday morning. I guess it's sort of short hand for "a surgical case" or "a surgical procedure". But it's pretty common around here to think of surgeries as discrete and countable things.
Why is this "Haqpu'" rather than "Haqta'"? Surely the surgery was intentional.
-pu' does not say anything either way about whether the action was intentional or not.
-ta' is explicit about there being an intention; -pu' is neutral in this regard.
So any -ta' can be replaced by -pu' without a contradiction, if you don't feel the need to emphasise the intentionality.