If we didn't inherit the sin nature from Adam then it would be like in Heaven when there were some angels fallen and some not. The earth would have been populated by some who never sinned like Christ (in his humanity) and some like Adam who did sin at some point in their life but repented and there would also be those who, like Lucifer, sinned and never repented. For those who never sinned there would be no need to break the power of the sin nature as they would never have acquired one and therefore would have no need to be raised from the dead. (they simply would never die) As for the second lot, we're back to the problem of how can they be judged fairly if their sin condemns them to death (and it does). How could they redeem themselves? Trouble is they can't. (keep in mind these are the ones who repented) They're stuck in death with no way out and they will eventually be thrown into the Lake of Fire. Also keep in mind the LoF was made for Lucifer and his angels. It's the place where evil is to be permanently and eternally separated from the righteous. The only way for this lot to come out from death is either God be shown a liar (not possible) and the wages of sin is not death but a temporary absence or The Lord deals with the problem Himself, in this case the Cross which doesn't compromise his word. Christ died because of our sin but was never bound to death because he had no sin nature. When the Father judged him (that is his humanity) it was met with the righteousness that comes by grace through faith for that is how Christ lived his entire life. Hence the grave had no power over him. As for the last lot, God is fair. He will make sure they know why they're condemned eternally and once again the only way they can stand before Him for the Final Judgement is for them to come out from the grave which means their sin must be paid for so they can be raised from the dead. After all, if we sin in the flesh, should we not be judged in the flesh? This way all is made visible to everybody and God is shown conclusively He is right in all he does.
Technically I believe it is truth that breaks the power of the sinful nature for that is how we overcome in our day to day life. The sinful nature which, is in the flesh, deceives us in our thinking. We each have our "fatal flaw". For some it is greed, another pride, another fear etc. which, is not to say we don't suffer from all those things and more but generally speaking there will be one flaw that outweighs the rest so to speak. Our bodies react accordingly in given situations and prompts us to think in terms of error. This is why we are to grow in the grace and knowledge of our Lord for He is the truth that counters the error and sets our thinking on the right path and this in turn keeps us from evil.
The Cross broke the power of death to which we were all bound. Sin isn't the big bogey man that people like to make it out. The real problem is evil. Evil is the thing to shun. Sin can be corrected but evil is, in it's nature, an unwillingness to be corrected. Adam's sin was to eat from the forbidden tree but his evil was to reject God's word (truth) and believe the Serpent's lie. There is nothing God can do to redeem or make amends or in anyway counter evil on our behalf for he would have to deny Himself to do so and He cannot do that. God can't reject Himself for us, hence the Lake of Fire. The only thing one can do with evil is to lock it up forever and keep it utterly separate, never to see the light of day (so to speak).
Don't know if this has made things clearer but I'm happy to keep sharing. You might see something I've missed or know something I don't.