National League teams spend on average something like $88 million, American League teams $97 million. NL teams may be less likely to pay 'everyday money' to a player, when they can instead pay a bench player.
And I just looked it up, the top 5 paid DH's were all making over $13 million. (
2012 MLB Designated Hitter Salaries - USATODAY.com) Which is absurd for a player who doesn't even play defense.
As much as a pitcher can get hurt hitting (like AJ Burnett did this year), the actual act of pitching is even more dangerous. So protecting your investment is moot. Bob Gibson broke his leg on a line-drive. Mike Mussina got hit in the face with a line-drive.
People just don't like seeing pitchers hit, lol. But it can be exciting, like when Joe Blanton hit a homerun in the World Series.
My only argument for the DH in the National League would be that it would even the scales when it comes to signing top-notch players. Someone like Pujols would be more inclined to stay in St. Louis (excluding the major money the Angels offered him) if he knew he could be protected in his last few years by foregoing the field and just hitting.