There are plenty of successful DTs who spend very little time on the offensive side of the LoS. A good example is Tony Siragusa. In about 75% of situations, the offense dictates the tempo of the play, genius, and that percentage is higher when playing from ahead.
Often times, getting upfield puts you at a disadvantage, and is even the worst thing a DL can do on, say, a trap play. If everyone thinks they're a pro-bowler, nobody holds their gaps and you get carved up - see the post-superbowl St. Louis defense for a good example of that.
Siragusa spent about 30 seconds total in offensive backfields the year that team won the superbowl - so I guess you wouldn't want him on your team. You're a resgular Bill Walsh!