I think that's true of (Dyalog) APL, but not of J [1]. APL follows the nested array model (that you describe), while J follows the flat array model that does have true scalars.

[1] https://aplwiki.com/wiki/Array_model#Flat_array_theory

It's certainly true that, depending on how the code is written, you may not be able to optimize out the language implementation from the compiled program. But that just turns into a link against a library with support for the language for your hypothetical compiled program.

That said, the compiler being hypothetical is a very real obstacle. But even there the problem is not that the language can't be compiled -- it's that no one has bothered to implement a compiler for it.

Anyways, if you throw in some ML type inference, and some tools for characterizing the resulting code and its interfaces, you can generate code from an array language which is quite similar to the code you would get from a variety of other languages.