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There was no Faith Militant for ages, the Targaryens took care of that. Only Cersei with her pissing contest with Margery hat this brilliant idea to bring them back.

"Art is magic delivered from the lie of being truth"

Even if Cersei did try it Joffrey would have destroyed the Sparrow and the Faith Militant before they ever gained significant power.
J-j-j-j-jingle bells. J-j-j-j-jangle bells.

The High Sparrow got in power due to Cirsei's bungling. She hoped to use him as a weapon against Margery and it backfired. Probably wouldn't have tried it if Joffrey was still alive and married to Margery.