I see what you're saying and yet, belief saves. Not work.
Some people who aren't really in Christ are those easy believers. They think , if I wear a cross and say I believe in Jesus I'm good to go. Then they are bad and go on sinning.
That's not belief that saves though. That's fun land worldly nonsense delusion that cripples and destroys.
However, belief is all that is required to come into Christ. Because Jesus did all the work for us on the cross. And our faith in that and our being in Christ occurs because it all started off with God the father giving his grace to the world as a free gift that would bear salvation to the world through the sacrifice of his son for all the sins of the world that would be taken upon him on the cross.
Being Jesus was God the father, in essence, literally, God who set the law of righteousness and the penalty for sin in the beginning, reworked that covenant law into a new covenant. Where the former penalty was paid in full by himself, as Jesus. He took back in other words what was the first law of sin and redemption. And he put in its place the covenant that said, all you have to do is believe you are a sinner. Believe you can renounce your sinful nature and ways, and believe in and on myself/my son, who you can cast all your past transgressions upon as that perpetual sacrificial lamb upon which those sins can be laid, and they will be washed clean by the blood that covers them for eternity never to be remembered again.
And now, washed clean you come into Christ as a new creation washed clean and always covered for your future transgressions by that blood, and the advocacy on your behalf should you slip up and sin because Jesus is our advocate with the Father. In other words, at least as I read it, God knows who are truly repentant and receptive to the new covenant and as such he knows when we do sin it isn't because we're that aforementioned fun land worldly in name only poser who thinks to play at what is often called, Pascal's wager.
That's why Jesus said, he knows his sheep by name and we know him and we follow him.
Wolves, the fun land type, in sheep's clothing don't fool God.
Having faith saves. And after we are indwelt with the holy spirit we're new creations. So we don't have those desires as that old self to be part of this world and sin. We are led to do righteous things. We endure this world through the leading of the holy spirit and in the end we are with the father.
We carry the protection and the wisdom to navigate the world within us. We are led to do good work because of the righteous leading that guides us toward that .
It isn't that work that saves us. Good works are a result of being indwelt and saved. Not a means of becoming indwelt and saved.
It doesn't get any simpler than John 3:16 and this, Ephesians 2:8-9 "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; not as a result of works, so that no one may boast."
For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord. (Romans 6:23)