[Scott from the Left Coast]

While it is easy to say that Frodo's mission is the most important -- that doesn't mean that assets are not needed in other missions, the success of which are absolutely necessary to the success of Frodo's. Without the defeat of Saruman, Rohan would not be free to aid Minas Tirith. Saruman was unwittingly (we think) providing Sauron with a second front -- dividing the enemy. Aragorn's decision may have been based on where he could provide the most service. Also, Aragorn knew that his future included a date with the army of the dead -- which were in the direction he would head in following the Orcs.

I think he at least suspected that Frodo's mission did not depend on the protection of his strength...but that in the other battles his strength might be decisive.

[HairOfTheDog]

One could propose that the single event that may (no spoilers, right) turn out to help the cause more than anything else is Merry and Pippin's capture... Captive halflings will grab the attention of everyone, and kept all eyes safely far away from the activity at Sauron's own border.