There are two factors that promote men's quest for salvation by works.
- Man ate from the Tree of Knowledge of Good and Evil. The result of this folly was that he saw that he was naked. Now, in Parable, "naked" is having your shortcomings revealed, and a garment is one's OWN works (whether Good or Evil). So Adam made a "garment of Fig Leaves", which satisfied Eve. But when God appeared on the scene, Adam, while wearing the garment of Fig Leaves, admited that he was naked. Innate in man is the poison of the Tree of Knowledge of Good and Evil. He intrinsically weighs Good with Evil - HIS Good, and/or HIS Evil - and like Eve, other men are satisfied by it. But God NOT.
- It is naturally abhorrent to men to tell them that they are sinners and in need of a Substitute Sacrifice for their intrinsic evil. Part of the fall of man was his SEPARATION from a Holy God. He is ever, even subconsciously, trying to restore that gap. But he will, through his pride, achieve it by himself
But the matter of works also plagues the Christian, as you rightly said in the OP. And a cursory study of the Bible seems to show certain scriptures agreeing with that. The answer is simple. What is difficult is to forget 1,800 years of Roman Catholic doctrine.
In Genesis 1:26-28 man was made for two things, (i) to be in the image and likeness of God to display him, and (ii) to be subduer and ruler of the earth, sea and sky. In 313 AD, Constantine percieved that killing Christians did not stop the spread of Christianity. So he did what was predicted by our Lord Jesus in Matthew 13. He declared Christianity a State Religion, and then allowed it to be "leavend" with all the pagan beliefs of the remaining 95% of the population. One of the most devasting doctrines that has "leavened" Christianity, is that pagans, who worship the heavenly host, changed point number (ii) above to say that a good man will, at death, go to a heavenly pavilion, or lodge. Subtily, God was made to be defeated because He could not get His man to subdue and rule the EARTH. He must save His man and then take him to heaven - and of course, leave the earth to Rome.
But if we believe that God is ALL-MIGHTY, then, like Daniel 2:44, Revelation 11:15 and Revelation 22:5 say, God's men will first subdue, and then rule, the EARTH. And it is here that WORKS come into play. In point number (i) above, for a man to be in the likeness and image of God, he needs God to (i) lift His retribution for his sins, and (ii) to infuse His LIFE into the man so that man is made partaker of the divine LIFE in order to display God (Rom.8:29; 2nd Pet.1:4). This putting away of sins and giving of divine life CANNOT be achieved by men-kind. It HAS TO be a work of God. And it MUST be imputed and NOT EARNED. This part of man's SALVATION is for FREE and is by FAITH - also a gift (Eph.2:8). But once the man is a Christian, he now is in line for co-kingship with Christ to subdue and rule the earth. For this, the man MUST SHOW THAT HE IS WORTHY. The parable of the Talents and the Pounds, plus various other parables show that a man must be PROVEN WORTHY. And that to be a worthy king with Christ over a city or cities (Lk.19:17-19), he NEEDS a rigorous TRAINING. God cannot afford to have His kings of this earth to do the same sinful and selfish things that the gentiles do now.
So for redemption, atonement, rebirth, and having the divine Life to be a man in the likeness and image of God, YOU NEED GOD TO DO THE WORK. But while under training, and at the Judgment Seat, wher it will be decided who gets a city, or cities, WHAT YOU DID COUNTS. So, if you examine all scriptures that require a man to be saved, they will EITHER address GOD'S WORK and a subsequent FREE GIFT, or they will address YOUR WORK during this age and whether you are fit to INHERIT the Kingdom that Christ will set up on earth. Try it and see if it works. You can even reverse it. Galatians 5:21 and Ephesians 5:5 show what will get you EXCLUDED, not from the divine Life, BUT THE KINGDOM!
Easy ... if you can forget Heaven and believe God's Word that man is for the EARTH.