Would it be possible for God to create a world that is perfect and in which humans have free will? Why or why not? And if so, why didn't he?
He is going to do just that. One day, this fleshly body will be changed, as I Corinthians says:
15:42 So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption: 15:43 It is sown in dishonour; it is raised in glory: it is sown in weakness; it is raised in power: 15:44 It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body.
15:45 And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
15:46 Howbeit that was not first which is spiritual, but that which is natural; and afterward that which is spiritual.
15:47 The first man is of the earth, earthy; the second man is the Lord from heaven.
15:48 As is the earthy, such are they also that are earthy: and as is the heavenly, such are they also that are heavenly.
15:49 And as we have borne the image of the earthy, we shall also bear the image of the heavenly.
15:50 Now this I say, brethren, that flesh and blood cannot inherit the kingdom of God; neither doth corruption inherit incorruption.
15:51 Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, 15:52 In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.
15:53 For this corruptible must put on incorruption, and this mortal must put on immortality.
15:54 So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
15:55 O death, where is thy sting? O grave, where is thy victory? 15:56 The sting of death is sin; and the strength of sin is the law.
15:57 But thanks be to God, which giveth us the victory through our Lord Jesus Christ.
15:58 Therefore, my beloved brethren, be ye stedfast, unmoveable, always abounding in the work of the Lord, forasmuch as ye know that your labour is not in vain in the Lord.
(King James Bible, 1 Corinthians)
The Bible says we will be changed, be incorrupt, that is sinless. Sin will have no more power over us. People mistake free will as being able to sin, and it is true to an extent. When one sins, they do excercise free will, but when they sin, they become a slave to sin, not free at all. But when we are changed, sin will lose its power over us, we will have free will, but we will not be brought under the power of sin, will not even desire or be capable of sinning. We will be free from sin once and for all. God will create a new heavens and earth and will dwell with us and He will be our God and we shall be His people, and it will be perfect and we will have free will, but our will will be His will, for sin and death and Satan and all that is bad will no longer have any place with us, we will be made glorified, incorruptible, immortal, and will know sin for what it is and it will no longer influence us. With Christ is liberty, we will be free, and one thing we will be free from is sin.