I think you are focusing on the theoretical aspect of partial application and missing the actual argument of the article which having it be the default, implicit way of defining and calling functions isn't a good programming interface.
I wrote a non-trivial lambda program [1] which enumerates proofs in the Calculus of Constructions to demonstrate [2] that BBλ(1850) > Loader's Number.
[1] https://github.com/tromp/AIT/blob/master/fast_growing_and_co...
[2] https://codegolf.stackexchange.com/questions/176966/golf-a-n...
They are not equally easy for me to use when I'm writing a program. So from a software engineering perspective, they are very much not the same.