Wow. I included אתהin my answer and it wasn't accepted. Is that really wrong?
Not really wrong, but in the past tense the pronoun isn't used. You would use אתה if you were emphasising "Why did YOU waste the time?"
First- and second-person pronouns are usually omitted from the past tense.
Should we be teaching מדוע here? I used that word for the last time in the market once and got laughed at for it because it was so ancient.
It's rare in daily speech, but is still common in writing (newspapers, books, etc.) and in formal speech, so I think it should definitely be taught. Just with a warning. :-)