It's actually not considering that this is an English translation intended for English "speakers", so appealing to them by translating a certain phrase in a common way would make the translation feel all the more authentic and closer to an official one.
I am American, and I agree that "You done yet?" i just fine. Partial lyrics from a Bart Simpson song, "Deep Deep Trouble":
Bart: So I'm in the front yard, mowin' like crazy,
Sweatin' like a pig and the sun is blazing.
Homer's in the driveway, getting in the car,
With Mom and Lisa, hope they're going real far.
The dad yells
Bart: and I go Yo
He goesHomer: You done yet?
Bart: and I go No.
So he goes
Homer: Oh! You're too slow.
Bart: So I step on the gas, to speed up the mow.
Didn't see that sprinkler underneath that tree,
Wham! Ccchhh! Pssshh! Raining on me!
I go Whoa, Homer goes
Now you can't go to the boatshow.