Problem with using Inquisition is that Mongols don't start with Doctrine so they can't initially build them. And between researching Doctrine, building Religious Persecutors and unrest using them causes that's lot of wasted time.
One possible solution would be to have STF require Animism civic instead of Paganism. Since Animism can't be switched back to and STF requires Silk, it would be unlikely that AI would build it outside Mongol territory. Human player could get it still with other civilizations but that would require one to not change their religious civic.