DK, no matter how good, will never beat a good (I put an emphasis on GOOD) D3 unless some sort of exploit against D3 is found. Yes, it might improve your metagame with DK, but fighting a D3 is not only a fruitless effort, but it does nothing more than improve the way you fight against D3 specifically instead of focusing on other characters.
You have to realize that there are match-ups where your opponent has absolutely everything against you. In this kind of situation, whether you're in it for fun or you're in it for winning, the smart thing to do would be counterpick. You're not gonna have fun in a match-up like this, nor will you win in a match-up like this. This is exactly why people pick up secondaries: for times when the **** hits the fan and there's no other option except lose, lose some more, and get your *** handed to you (Which is not fun in a tourney setting).