You do realize don't you, that those letters you are referring to were sent to those who were brought up under the old Covenant. The sacrificial blood of Christ was for those that were under the first covenant.
1 John was written to believers. Yeshua is not only an atoning sacrifice for believers, but for the whole world (including those who were not under the OC.
1Jn 2:2 And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.
Hebrews 9:15
And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance.
I was born into the New Covenant, I was not redeemed from the old testament and the Law of Moses. I was redeemed from the sin of Adam's transgression.
How were you redeemed from Adam's sin?
Rom 5:8 But God commendeth his own love toward us, in that, while we were yet sinners,
Messiah died for us.
Rom 5:9 Much more then, being now
justified by his blood, shall we be saved from the wrath of God through him.
Rom 5:10 For if, while we were enemies,
we were reconciled to God through the death of his Son, much more, being reconciled, shall we be saved by his life;
Rom 5:11 and not only so, but we also rejoice in God through our Master Yeshua Messiah,
through whom we have now received the reconciliation.
Eph 1:7 in whom we have our
redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace,
Col 1:12 giving thanks unto the Father, who made us meet to be partakers of the inheritance of the saints in light;
Col 1:13 who delivered us out of the power of darkness, and translated us into the kingdom of the Son of his love;
Col 1:14
in whom we have our redemption, the forgiveness of our sins:
Hebrews 10:15-18
Whereof the Holy Ghost also is a witness to us:for after that he had said before,
This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; And their sins and iniquities will I remember no more. Now where remission of these is, there is no more offering for sin.
The phrase in bold simply means we don't need any other sacrifice for sin and that Yeshua need not sacrifice himself over and over again for each sin. His one time sacrifice and shed blood continues to cleanse the sinner throughout his life. However, if we reject his sacrifice and renounce him as our Savior and atonement, then his sacrifice no longer remains for us. It is withdrawn and we return to being dead in our sins with no blood sacrifice.