It's something worth discussing. Unless your team has every other hole filled, spending a large chunk of cash on a designated hitter is dumb. Why? Let's run through the reasons...
Fielding, the DH does none. With limited financial resources the top priority for any team investing in a positional player should be getting a player with offensive and defensive skills. Further, since the fielding ability is irrelevant to a DH, this increases the talent pool in which DHs can come from. Players like Travis Hafner, Jack Cust, and David Ortiz are prime examples of what you can find when digging through the DH talent pool, virtually every good hitter is available, and whether they have a weak arm, slow feet, or poor speed is moot as long as they can produce at the plate.
Salary. With a widened talent pool this increases supply, and should decrease the price. When was the last time a catcher in his prime hit the free agent market? Mike Piazza was close before being traded. Early-30's Pudge Rodriguez? Former corner outfielders or third basemen with eroding defensive skills are usually signed as designated hitters, along with players with no glove to begin with. Why pay for something so readily available? Being a DH also seems to lower the player's trade value.
With that being said, which teams can afford to pay a DH a worthwhile sum of money? The Jays and Rays come to mind. Both teams are defensive heavy and lack gaping holes at any fielding or pitching position. Adding offensive should be a priority for both, especially Toronto, and if one of the available DHs pushed for a short deal in order to test a hopefully resurgent market within a year or two, that just works into their hands even more.
Paying big bucks for a DH: generally stupid, unless you have every other position adequately stocked.