According to mainstream Christian thinking (Protestant, Orthodox, and Catholicism), do i inherit Adam's sins but not Adam's good deeds?

I have have read the posts related to this question, but they do not tackle this issue from the same angle. For the related questions i have seen, the focus was only on why we inherit Adam's sins. **I flip and ask why we don't inherit Adam's good deeds**? For those that may say we inherited his "sinful nature" or capacity to do evil but not the original sin itself, that doesn't tally well with the Protestant concept that flows from "we (including children), have all sinned and fallen short of the glory of God". **Personally, I believe children come from God pure and without sin.** **I believe Adam's sins were his own sins (the "original" and any other sins), and I should not be asked about them; because Adam was a human being with his own issues, and I have mine**. To argue otherwise is to contradict Ezekiel 18:19-21 **"The soul who sins shall die. The son shall not bear the guilt of the father, nor the father bear the guilt of the son**. The righteousness of the righteous shall be upon himself, and the wickedness of the wicked shall be upon himself.."