In both movie and book, the entire Haradrim army fought from the "war towers" on mumak backs. They did not heavy infantry, cavalry, or artillery, only this heavy cavalry in the form of oliphaunt-born seige towers. Its not that the Haradrim needed to find a purpose for their mounts, only that it was the only thing they used. Do you think they're going to leave out their most powerful weapons (which just happen to be Rohirrim-crushing tusk-tusking horse-trampling mumakil) out of a battle because they are not tactically sound. Plus, once these beasts got near the wall, the towers on their backs could shoot nearly endless volleys of arrows from protected areas.
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"What mortal feels not awe/Nor trembles at our name,
Hearing our fate-appointed power sublime/Fixed by the eternal law.
For old our office, and our fame,"
-Aeschylus, Song of the Furies
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