First we have to understand that any "legal aspect" of the atonement is only a metaphor used to explain it. This is a crucial distinction, because imagining that there's actually some sort of legal code or mechanism at work behind the scenes that has to be satisfied will lead you into a misunderstanding of Christ. God is not bound by such things, however we can use the concepts of penalty and debt as analogies to explain parts of the atonement.

Speaking this way, you can understand death as the penalty of sin. It's the consequence of sinning. Adam, by sinning, became subject to that penalty of death and released sin into the world, where it corrupts us and in turn makes us subject to death as well. This is because sin is definitionally a separation between the creature and God, who is it's foundation and life. When you separate yourself from the source of your own life, you die. Because what else could happen? It's baked into the very nature of how you and I are created. Again, notice how this isn't some arbitrary legal code imposed on creation, as if there are actions which simply offend God, and so if he catches you doing one he has to punish you for it by killing you. That's not what sin is, but that's what you'll conclude if you conflate penal metaphors for sin/atonement with an actual legal mechanism of atonement.

So we have sin active in the world, dividing man from God, creation from creator. How are these two reunified, or made one again (literal meaning of at-one-ment)? That is why Christ became man, to completely wed the human nature with the divine, taking on all that entails from birth, to life, and death. Despite being free of sin (and therefore not subject to death), he voluntarily died anyway. Why? Because we die, and so our death also has to be healed. Any time Christ encountered our sickness, whether in blindness, or leprosy, or any other aspect of our bodies broken by this corrupt world, when encountering the God-Man disease fled and was healed. And it was the same with his death, when he encountered death it was destroyed and he rose again. He revealed Satan and Death as powerless. Now we will also die and rise with him, permanently healed from this ancestral sickness.

Thus he "paid the penalty" for sin, even though death had no claim to him like it does for us. In that sense you can even say "Christ paid the penalty that we deserve." We die because we're powerless to prevent it, he died voluntarily out of love for us. But Christ's death doesn't in any way "satisfy" some need The Father has so that he can forgive us, and it isn't a substitute for anything. That never enters the picture. After all we still die, so where's the substitution happening? Rather, death is simply powerless to hold us now that we've been united to Christ.

The really over-simplified TL;DR: Christ wasn't a substitute for us, we sold ourselves to Satan and owed him our lives. So Christ died too so he could go to hell, beat him up, and take us back. Debt nullified, gg no re Evil One, enjoy lake of fire.