I John 2:2 reads (without the italics of the KJV)
And he is the propitiation for our sins: and not for ours only, but also for of the whole world.
και αυτος ιλασμος εστιν περι των αμαρτιων ημων ου περι των ημετερων δε μονον αλλα και περι ολου του κοσμου
The wording 'the sins of' (the whole world) is not in the original Greek text. I am referring to the TR, here.
'For of the whole world' (idiomatically, in English, this may be rendered 'for that of the whole world) refers to the sin of the world which is also spoken of by John the Baptist :
Behold the Lamb of God, which taketh away the sin of the world. [John 1:29 KJV]
John speaks of two different things in 1 John 2:2 :
And he is the propitiation for our sins, and not for that of us only, but for that of the whole world [Literal Rendering].
He speaks of sins firstly, the matter of personal culpability, one's own sinful activity. Then he speaks of that which is corporate, true of all humankind due to the deceiving of Eve and the transgression of Adam.
Paul treats of this in detail in Romans 5:12-21, the matter of headship, either of Adam or of Christ. They under the headship of Adam are under sin and, thus, under the sentence of death. They under the headship of Christ are under the ministration of 'reconciliation' (actually, restoration - it is katallasso).
The benefits and blessings of 'reconciliation' (restoration) are realised in faith and received from Christ himself, as ministered through the Holy Spirit.
'That of the whole world' is dealt with in the death of Christ (as opposed to the sufferings of Christ prior to death which deal with the sins of men, their personal actions).
The liability of sin entering the world, the liability of flesh and blood and its propensity, the liability of the created creature with regard to the tree of the knowledge of good and evil : all is dealt with in Christ, in his death.
As the question quotes, the body of sin is done away with, in the death of Christ he being 'made' sin, 2 Corinthians 5:21. That is eradicated in the death of Christ, sin being contained in him, within his humanity, and being eradicated in his own death.
But this is a matter of headship.
They who are under the headship of Adam, remain subject to death, because of sin.