The whole key to the strategy was to distract Sauron from the Hobbits' Quest. So it was essential to have the King and Gandalf over on the other side of the river, both to save Minas Tirith, but also for the purpose of distracting Sauron.
Also, the Quest into Mordor is really one of secrecy. Aragorn is perfectly suited for this, except for his size, given his experience in the Wild (after all, he found Gollum in the Dead Marshes). But the Hobbits, with the guidance of Gollum, were suited for this as well, basically another story where the Hobbits are brought along because of their "burglar-like" qualities--small size, stealth, noiseless movement...
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