While requiring more than "a simple majority" seems like a mechanism to prevent certain regrettable outcomes, it really doesn't, it's just a line in the sand. We should oppose a million people voting to execute one innocent just as fervently as 500 people voting to execute 499 innocents, the problem isn't the ratio and so a correct solution can't be about the ratio.
Consensus is great, I love consensus - if you can find a consensus that's brilliant. But super-majorities are not a consensus. And of course when you really do have a consensus it tends to be naturally enduring anyway. I am very dubious of people who imagine that there might be a consensus for policy one minute and then shortly after the consensus is gone. I think there was only ever some clever sleight of hand to deliver the illusion of consensus at all for some purpose.
When contemplating making major changes in governmental structure, consensus would be best, but super majority is probably second-best and first-achievable.
You can’t run a country needing 100% consensus of over 200M people.
Not everybody agrees, for example in UK the parliament is the ultimate sovereign and it is not bound by law other than self restraint.