It wouldn't really make much of a difference, if any. For source files, anyway - more complicated diffing helps for files we consider just "binary" now but that are actually structured.
Pijul's pushouts are unrelated - that just allows a line in a file to be ambiguous, rather than definitely being one line.
You say Pijul's pushouts are unrelated, but their construction depends on a very line-centric definition of patches. Wouldn't it need to be made more complex to accomodate tree patches?
No? The concept is that a unit of diffing (a line, or a tree node in your hypothetical tree-diffing approach) can be ambiguous until another patch resolves the ambiguity.
In the vaguest sense, sure. But if a file is a list of lines, this "ambiguous file" is a digraph of lines. If a file is instead a tree of strings, what does an "ambiguous file" look like? See this paper which was the source of some of the main ideas of Pijul, and in particular, note that its extension to structured data is listed as "future work", which means it probably hasn't been done yet.
Pijul's pushouts are unrelated - that just allows a line in a file to be ambiguous, rather than definitely being one line.