To be sin-conscious puts your focus on something that doesn't define you.
Language matters. Let me put two scenarios. Someone walks in the Spirit and does not sin. They maybe tempted but as far as their conscious is telling them, they walk in holiness. Sin is not an issue, their focus is on the Lord, serving needs as they come up.
Another walks in the aspirations of spiritual maturity. Though they want to walk in deep fellowship, the are beset with worries and failure, often dropping into envy, lust, covetousness, occasionally lying, flirting. In their heart they feel is with Jesus but something is wrong. They are conscious of sin, yet cannot quite put their finger on it.
Now for them to not be sin conscious would be a lie, and if they stay where they are they will fall away, because they are denying the very faith they claim to follow.
To the first person, sin consciousness helps confirm their walk in the Lord, it keeps them true. Now many would deny this is even possible, but it appear Paul and the apostles would say this is their walk in the Spirit.
The second person is blinded by this concept of lack of sin consciousness. For them the step of transformation they need to take has been taken away. It plays to the lie that this world has real value, that you are measured by your wealth or influence. It also gives them reassurance they have arrived when the journey is still to come.
So rather than being helpful it is a lie of the enemy. Sin is death, it destroys everything it touches. Only slaves who fear the prison of sin need to invent such a concept and it is a license to ignore besetting failure in peoples lives. But for those who have given up already, who cannot abandon Christ yet their lives feel empty it is like salvation.
Jesus talked about evil doers, so this is what we must never be a part of.