What is the real benefit of scope extrusion in the Pi-calculus? I read that it adds more flexiblity to the overly restrictive prior process algebra where the scope of a newly created channel was limited. However, taking a first serious look into Pi-calculus, I came to think that this $\nu$-binder is a source of confusion between channel names and bound variables, which should be considered separately.
There are two binders in pi-calculus. One is a normal binder (just like the one in lambda calculus) in the receive $c(x).Q$ where $x$ is bound in $Q$. However, $(\nu x).P$ is a very strange binder because the scope of $x$ can extend over other parallel processes by an axiom, which is just strange, reminding me of dynamic scoping.
IMHO, this is all due to overloading variables and channel names. If we separate the notion of channel names from variables, we can make the $\nu$-binder a true binder where the variable following $\nu$ is a normal bound variable and we only need to add a reduction rule for it, which is just like the reference cell allocation in ML: $$ (\nu x)P \longrightarrow P[c/x] $$ where $c$ is a globally fresh channel name. Then, everything made sense to me.
So, what is the benefit of having this strange axiom for scope extrusion when we can simply model it as new channel creation, which to me is much more intuitive and also closer to real implementations.