I don't disagree. Try to mute your "mathematical thinking" for a second and read it as an ordinary person, with a focus on practicality. It just doesn't look right.
If it did look right to me, I wouldn't be sitting here typing this all out. I would be silently agreeing with the mathematical point of view.
That's what tells me this is a likely source of confusion and error.
I'm not saying it should be false. It's the law of the excluded middle that forces us to make a true/false decision, in which case I can agree that, for mathematical reasons, it should be true.
For practical reasons, it might be better for it to be false. That would require some empirical research on whether this could actually prevent harmful behavior in practice.
From a design perspective, I would argue that "all" should not be defined for empty lists, because that forces people to consider whether the often-forgotten "empty list" edge case might cause an issue.
If it did look right to me, I wouldn't be sitting here typing this all out. I would be silently agreeing with the mathematical point of view.
That's what tells me this is a likely source of confusion and error.