I played 1e and 2e. To death, so to speak. In theory they were more lethal than in 5e. In practice, not for us. I think it really varied by campaign. But what I find hyperbolic are your claims that over-generalize, such as "More then one adventure had an "on the edge" encounter, where foes would try to knock PC off a cliff or into acid pools or such. 5E does not even come close to such encounters." That's just not true; there is nothing in 5e preventing you from building such an encounter; in fact, here is one that I built not long ago:
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Room full of acid, characters trying to get across via precarious perches, and an ooze trying to drag them in. 5e.
I pretty much agree with Snarf's OP. On paper AD&D looked positively lethal by today's standards, but in practice it really depended on the group, and most folks adopted rules and play styles that ameliorated the body count. Gygax himself had many characters that he played for years. 5e is generally less deadly but again, that comes down to table culture. If my group wanted to create a hyper deadly campaign using 5e, it would not be hard to do so.