I believe it was essential for Aragorn not to follow Frodo into Mordor. By pursing Merry and Pippin he was able to aid in the defense of Rohan, then reveal himself to Sauron in the palantiar making him a bit nervous I guess (made him attack faster and look away from where the two hobbits were approaching), and then take the Paths of the Dead to prevent the corsairs from attacking Gondor.
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"Dic, hospes, Spartae, nos te hic vidisse iacentes dum sanctis patriae legibus obsequimur."
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