I don't remember off the top of who first showed that parallel computation has no 'good' encoding into functional computation (lambda-calculus). I'll try to dig out a reference and post it here if I find it.
But the upshot of all this is that message-passing is more fundamental than functions / function application.
[1] C. Hewitt, H. Baker, Actors and Continuous Functionals.
[2] C. Hewitt, Viewing Control Structures as Patterns of Passing Messages.
[3] R. Milner, Functions as Processes.
x!<a> | y!<b> | x?(c).y?(d).P
Conversely, I don't think linear logic is a good typing system for pi-calculus for a variety of reasons: among them that linear logic does not track causality well, and because it doesn't take care of affine (at most once) interactions well.
(Also, to be clear and with reference to other threads we've conversed on here, I think of linear logic and pi calculus, even if they aren't well-corresponding, as fantastic, unavoidable examples of non-function-application style programming.)
But this is just a way of thinking that makes me feel comfortable because I like to have a physical model. If someone else is happy with function application as being the fundamental building block then I have no problem with that. However you said that "there are theoretical reasons to believe that message passing is not function application (while function application is a special case of message passing)." I would be interested to get more background on this. Would you have any references for this? Thanks.