God has always wanted us to do good works. We do those works regularly in theory, but often fail through our nature, which is a sin. That makes us sinners, and the wage of sin is death...
In the Old Testament that death was passed on to an animal that was sacrificed, then God, not liking the "sin, sacrifice, sin again" cycle, sent His son to be the sufficient, sacrificed lamb for one and all, should they believe in Him. Not just believing in His existence, even the demons do that, and shudder. They know what's coming next!
That faith will involve giving ourselves to the Lord and living as He wishes to the best of our abilities, works will inevitably be a part of this and will be seen, the same way our words display what's in our hearts.
That's what saves, Jesus and faith in Him. That faith is shown with works, but the works themselves can't save as we've failed, fallen short of perfection and are sinners. God did it and we're recipients. He saved us and still wants us to do good, even though we fail. It's right to do good. It's just that we failed to do it all the time and thankfully accept a saviour in Jesus.
Standard
An extension of your premise is warranted. The least recognized concept of salvation is that we are saved body, soul and spirit. Our resurrection will not be just the part of our grey matter that "contains" what we call faith. We are a soul that has a body, they are indivisible, thus we are indivisible. We can not "get our souls saved" without being fully bodily saved. We can not just claim to love God in our minds without loving God with our entire being, body and soul.
In the same way faith and works are inseparable but there is actually a bigger and more unifying framework that is left out our "Salvation by".....dogmas. Jesus and Paul make it clear, that the reborn person, the converted person will come to understand that salvation at its core is only about one thing...Love.
We are to love like Jesus loved, who he loved, how deeply he loved, how sacrificially His love is. It is easy to dismiss the Hebrew Bible model of sacrifice because we restrict it to some kind of animal thing. It was a long learning curve to teach humans that any right relationship with God is based on our sacrifice, often many kinds of sacrifice and always sacrifice for the right reasons. Many sacrificed their 1st born sons via pledging them to God for life. All who sacrificed weekly cost them time, money and even food off their table. At the end of that age, God showed us what the ultimate sacrifice was in Jesus the Christ. If the cross of Jesus does not teach us that love requires loving sacrifice then we have no hope. If it does not teach us that we too are called to take up our cross daily and deliver sacrificial love then we have purposefully reject the heart of the Gospel of Christ.
We have replaced all concept of our sacrifice. We reject all important forms of sacrifice. We "are guaranteed" a free ticket to heaven by nodding to a 60 pulpit prayer. Thus our "sacrifice" is that we "make room for Jesus in our heart."
Paul made it clear, if your horizontal and vertical relationships in life are not driven by love then it is just "noise." Jesus was crystal clear, if you love God you must obey God and submit to His transformation of your life. If you love God you must love your neighbor. Jesus story of the "Good Samaritan" is a story we love to tell but it is usually taught as a story showing the hypocrisy of the Jewish clergy. Is not. It is a clear statement that loving your neighbor requires personal involvement, personal care and an uncapped expenditure of money to bring God's love to those most in need. In 21st Century Protestant and Non- Denominational Christianity we assume these people are the responsibility. This is based on the delusional belief that we are in the "saving souls" business.
And here we sit trying to split hairs with 45,000 competing Christian dogmas trying to find comfort, self-interest, self-righteousness, convenience and personal freedom of choice in all matters. Way more that half of those attending Christian service don't even give money yet we disparage those O.T. Jews who paid 10% of all they owned to support God's work and added a weekly sacrifice out of their flocks, cattle, crops showing weekly they were willing to take food off their table weekly to obey God.
The New Testament is clear. There is no division between our souls and the rest of our body. We are souls. You can attempt dissect humans into physical, mental and spiritual components for purposes of making your dogmas work. That is why there 45,000 competing Christian dogmas. We are trying to recruit people of the same race, same income level, same politics, same education level, same knowledge worker and same culture. That is why our Protestant and non-denominal churches look the way they do. There is zero correlation between super comfortable dogma based recruiting and sacrificial and loving embracing of all who seek God.
If you think what you define as faith alone will save you, read 1st Corinthians 13 and Matthew 25.
Paul consistently teaches that salvation is by faith alone, apart from works of any kind. When he says “works of the law,” he means the ceremonial or legalistic works that some were trying to rely on for righteousness, not the good works that naturally flow from faith. Faith is never “completed by works” in the sense that works earn salvation. James 2 shows that works demonstrate that faith is real, they don’t produce justification. Abraham was justified by faith (Romans 4:3), and his works proved that faith was genuine. In other words, works are the evidence of salvation, not the cause. Paul mentions works all over the place, but he consistently separates them from justification. Works follow salvation, they do not make it happen.
Paul never says "works of any kind". He is helping Jews understand that "works of the law" and works oriented thinking will not save. If Christianity was against "works based religion" then Christ did not have to die on the Cross....the ultimate work of love. He just need to tell people to accept him in their heart...