Part of that missing atmosphere was that in D1 (and to a lesser extent D2), you were a weak human and death was around every corner. You might walk into a room and near-instantly die. You spent a lot of time running for your life.

Contrast that to D3, where I literally beat the game the first time without using a single health potion. You were a super-hero who could punch a skeleton and send the pieces flying at level 1. And while I can certainly see the allure of such experiences (hell, I enjoy them too in other games), it was not what I wanted from a Diablo experience.