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The good advice that Casper and David gave -- don't give Opp a good 6 from the bar -- is a factor in many hitting decisions. It doesn't seem to me that factor gets to the heart of the matter here, however, given that White's 6s from the 24pt are already blocked.
In the (variant) right-hand position, instead of running with 63, Opp has (illegally) passed her turn (done nothing), and Blue must choose between 63D and 63S (he is not allowed to play Z or R). This is effectively 1 pip different from the main position (on the left).
Because Blue owns the bar point as well as the 6pt, in either position 63D weakens White's 6s. White will hit a fly shot with 63 instead of 64 (wash), and her 65 is blocked instead of her 62 (washy). Finally, the net effect of 61 66 is unclear. From that surface analysis it is hard to tell on balance whether D's effect on 6s is bigger on the left or on the right.
As we don't have comparative rollouts, let's resort to XGR++ evals: [D X58] on the left and [D S40] on the right. Does the 6-from the bar issue account for the .018 difference in margin? Even if that allocation were clearcut, the 1 pip difference in the race (motivating 24/18 more on the left than on the right) is responsible for at least some of that .018 difference. More importantly, the other .040 difference is still to be explained.
Let's consider Tim's reason: 13/7 helps the blitzing chances. Not only does 13/7 add a checker to the zone, but it deprives White's counterhit on her 7pt from interrupting a potential blitz. In the left-hand position, White might enter without anchoring (or even fan), whereas in the right-hand position, White can stubbornly cling to her 24pt anchor if she chooses, aiming to win a priming battle while substantially stuck in the race.
At both dmp and gammon save in both positions, D and S are within .002 of each other (by XGR++ eval). This suggests that for money, a strong incentive for 13/7 is the greater chance to win a gammon. Evidently, though, the additional gammons don't come mostly from near-term blitzes (i.e., due specifically to the fact that White is not currently anchored), because most of 13/7's edge (.040 out of .058) also exists in the right-hand position where White is already anchored.
I think the simplest explanation is that 24/18 is a relatively poor 6 (except at dmp and gammon save, where racing is emphasized), giving White a useful tempo-hit with a 6 or a 1 without sufficient cause. As David implies, 13/7 is an even worse 6 (than 24/18) in most early game positions because the offensive bar point is not yet made. When the bar point is made, 13/7 is often a strong follow-up even when the opponent is still anchored (though less so) and even when it strips the midpoint.
Speaking of which, how does stripping the midpoint figure into the equation? On that issue, here is food for thought.
Nack