The Podlings taught Kira to call the animals, and she uses the ability to get them to break out of their cages, attack the Scientist, and free her before she gets her essence completely sucked out. Couldn't the countless Podling captives before her have done it themselves?
Because they didn't have a cheerleader like Kira did.
As the Scientist's own words state that gelfling essence is more potent than podling, she may be the only victim of the device who lasted long enough even to make the attempt.
If the Mystics are supposed to be so supremely benevolent, and they knew about their link to the Skeksis and about the horrors their counterparts were perpetrating, why didn't they just selflessly commit suicide a thousand years ago to spare the gelflings from genocide and the podlings from enslavement?
Note that the split gave the Skeskis the lion's share of the intelligence and the urRu have wisdom but not the knowledge of how to apply it - they may not be capable of this level of forethought.
Word of God says that the Mystics lacked the will to act, above all else. The Skekses represent the power of will and the desire to act; the mystics represent the wisdom and understanding of right action, but have no will to accomplish it.
Or perhaps the Crystal is an artifact that is necessary for the continued existence of the world. If the urSkeks were to all die, the Crystal may shatter completely, plunging the world into a cataclysm. We've all seen the effects that screwing around with the crystal has had on the rest of the world.
At the very least, the mystics did represent some balance against the Skeksis. Even assuming the mystics were willing to commit suicide, they'd essentially just be removing both factions from Thra, but still leaving the after-effects of the Skeksis' rampage. They'd just be committing the same sin that created them all over again: inflicting their will upon the world, heedless of the costs.