Odd that you say that. I always thought of Papi as a below average but adequate first baseman. He'd never win a Gold Glove, but if he was a NL player he would have played first base a la Prince Fielder and everyone would have just rolled their eyes when the big man muffed a throw to first and argued he didn't do it enough to make up for his value at the dish. He didn't play 1B more in Boston largely because of size and health concerns, not necessarily the glove which I've never seen be a liability on the field when he did play
In short the guy's only a "no glove DH" because we can afford to do it here in the AL, not because he couldn't play defense if he had to -- and indeed, when he's had to he's generally proven he knows what to do. That's exactly the kind of DH we'll keep seeing, I can give you one pretty young example, Billy Butler of the Royals.