According to this awesome work by Huckleberry (and biggerme):
http://www.ootpdevelopments.com/boar...56#post4189856
there is a factor of 9 for 2B, 8 for SS, and 3.25 for 3B. 1B has a different calculation but the TDP rating is in there (not sure off the top of my head how that compares to the ratios for the other positions). C is not impacted by TDP rating.
For a 3B, you could say TDP impacts their awareness to see a double play is possible (maybe the runner is close to the bag but their arm is strong and accurate enough to get them). There are also DP at 3B/Home, there's a skill to leading the 2B/SS to the bag to start it, they could have to charge the ball and barehand it, etc. There are a bunch of skills that could impact DP besides the pivot part, which is why the 2B/SS are higher weighted but the 3B is still involved.
For 2B/SS, the footwork on the pivot play, catching a ball while the runner is right on you, touching the bag and throwing all in one motion, etc. is a definite skill that's different than fielding a ball and throwing it.
For a 1B, you could say that they have to start some DP as well although much less common.