I see their nakedness as the loss of God's covering. They knew they had lost it, and were ashamed knowing their disobedience caused it. I have asked that question before, too, about why did they not eat of the Tree of Life? Especially since we are told man is a slave to sin due to his fear of death. Certainly, it seems this was part of their motivation. But if they did not want to die, why not just eat of the Tree promising Life? Well, they also wanted to be like God, and God confirmed that happened, in knowing good and evil. They decided for themselves what was right and what was wrong... Adam deliberately choosing wrong, and Eve being deceived. God temporarily covered them, with the skin/s of a sacrificed animal, foreshadowing the covering we find in the shed righteous blood of Christ. There is a lot to unpack there! Then begins the long hard crawl through history to where we are today...