Yes & No. While you could say that the only way to get rid of all suffering would be to root out free will, (and effectively root out real people as they are "constituted" in the process :) ), that's NOT the only way to get rid of all suffering...at least for some.
Imagine a missionary going into a leper colony. He successively asks over the course of years 10 female lepers to marry him. He assured each one that while his present calling could not be ignored, one day he would whisk his bride back to the mainland, where he promised she would be treated and cured of leprosy. The first nine reject him, refusing to believe his promise. The 10th accepts.
The pain of rejection was lamentable, especially when the groom knew each one could be cured. Yet, in light of his eventual bride, he did not regret the rejection-filled process.
The same is true of our Lord Jesus, who both created us and serenades us to be His now and in heaven. He created us knowing the first parents would abuse their stewardship of free will; and He created us knowing that most of their children would reject Him. Yet, He saw the bride from afar, and said, "She's worth it all."
Of the 12 times Jesus used the word, Gehenna -- the Greek word coming to symbolize "hell" - all but one came from Jesus' lips. He discussed "everlasting fire" and "everlasting punishment" in Matt. 25:41,46. Therefore, God knew all suffering would never be averted. And, in fact, He knew their suffering would be "everlasting" (what is "life" outside the Life-Giver, after all?)
But He knew all suffering for some would cease. Jesus, by suffering Himself, redeemed suffering. He devoured it for those who would trust Him to do so in their own personal road of suffering. 'Tis too bad, it's so few, who will trust Him to cure them of their spiritual leprosy:
13"Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it. 14But small is the gate and narrow the road that leads to life, and only a few find it. (Matt. 7:13-14)
True enough. I never said everybody would always suffer, only that suffering cannot completely disappear as long as free will is around to muddy the waters.