But still with the sentence of death.

The death sentence is based on past sinning - not current, ongoing sinning.

Past sin affects our current condition.

And for eternity. However, the atoning blood of Jesus does not cover the unholy clamorings of sinful flesh. It is not necessary. We are not guilty of sinning based on the fact our fallen flesh tempts us from within. Which is why Jesus was able to inhabit sinful flesh without incurring guilt. He was tempted from within just like a born-again believer.

I should have been clearer. Past sin affects our current condemnation.

What do you mean? As you know, past sins pardoned incurs no guilt or condemnation. Only willful, ongoing sinning incurs guilt and condemnation.

If not for Christ's covering grace, our past sins would kill us today.

True. If Jesus was not the Lamb slain from the foundation of the world Adam and Eve would have perished and none of us would have been born. Jesus cannot cover unpardoned sins or willful sinning. Jesus does not have to cover the clamouring of sinful flesh.

I could agree with that if I believed that sinful flesh did not clamor for sinful things. But I don't.

Sinful flesh is not a sentient being. It does not have a conscience. It cannot form character. It cannot sin. It does not need a Saviour. It can only tempt us from within to be unlike Jesus. It is not a sin to be tempted. Which how and why Jesus possessed the likeness of sinful flesh.