Why do you need to prove no correlation? Even if there's a correlation, unless that correlation is extremely strict, there is some risk of a super-intelligence turning nasty. And a strict correlation is simple to disprove with, say, humans and bonobos. Humans fight and hurt each other, while bonobos are basically the "peace and free love" hippies of the primate kingdom.

And orthogonality is not about ethics, but about goals. If you can have three very intelligent people, one of which tries to become an industrialist in order to become as wealthy as possible and live out their days in luxury, another of which decides to become a scientist and help humanity as much as possible, and one of which decides to spend their life building model trains, you have proof of orthogonality right there.

Unless you get a super-intelligent AI whose goal/behavior is exactly something like "always listen to humans and do what they say, but temper that by not hurting people, and don't try to get too far ahead of them and predict what they would want, and don't try to accumulate too many resources in pursuit of your goal, and also keep in mind that humans may try to invent other AIs may try to gain more resources in pursuit of their goals, and try to stop them if they go wild, but again don't go too far" and so on, for all the things I haven't even thought of but that are are also important, then you may have a really big problem.

If we can invent aligned AI, that will help a ton with all the other existential risks. If not, unaligned AI is the existential risk to end all others. Maybe things are changing fast enough now that the variance in our outcomes is so high that we're guaranteed to end no matter what. I hope not.