However

What we do see is a bunch of mathematical disciplines that end up creating properties like: AND, OR, Universal, Existential, Implication, (and a few others). They end up in places like: set theory, type theory, category theory, various logics, lattice theory, etc.

Now, maybe they're only copying one another and this is more of a memetic phenomena. Or maybe they've hit upon something that's important for human comprehensibility.

That would be the 'evidence' of the positive effect of ADTs (scare quotes because it might just be math memes and not fundamental). But we can also think about what I feel is legit evidence for the negative effect of lacking ADTs.

Consider what happens if instead of having the standard boolean logic operators and, or, not, xor, we only have the universal not-and operator. Now a straightforward statement like: A && B || C becomes (((A !& B) !& (A !& B)) !& ((A !& B) !& (A !& B))) !& (B !& B) [I think...]. It's more complicated to tell what's actually supposed to be going on AND the '&&' simulation can get intertwined with the '||' simulation. The result being that requirements changes or defect fixes end up modifying the object level expression in a way where there is no longer any mapping back to standard boolean logic. Comprehensibility approaches zero.

And we've seen this happen with interfaces and inheritance being used to implement what would otherwise be a relatively simple OR property (with the added benefit that pattern matching ADTs often comes with totality checking; not something you can do with interfaces which can always have another instance even up to and including objects loaded at runtime).