Is scope extrusion necessary in the Pi-calculus?
If we separate the notion of channel names from variables, we can make the ν-binder a true binder where the variable following ν 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:

(νx)P ⟶ P[c/x]

  
  where c is a globally fresh channel name. Then, everything made sense to me.


You are basically correct. 

The reason most people don't do this is that to model your side condition "where $c$ is a globally fresh channel name", you need to give an operational semantics for the $\pi$-calculus which tracks the set of names $\Sigma$ allocated so far. I.e., the rule above would become:

\begin{array}{lcll}  
  \langle\Sigma; \nu x.P\rangle &amp; \to &amp; \langle\Sigma \uplus \{c\}; P[c/x]\rangle &amp; \mbox{where } c \notin \Sigma
\end{array}

Then you'd also need a condition that a configuration is well-formed if the set of names $\Sigma$ is bigger than the free names in $P$, and you'd also need to prove some equivariance/permutation lemmas that configurations and reduction sequences are stable under finite permutations of names. 


You get this all for free from the $\alpha$-equivalence of $\pi$-calculus terms, at the price of introducing the (admittedly somewhat ugly) scope extrusion rule.
However, if you don't like it, you're in good company. Bob Harper does things the way you suggest in his book Practical Foundations for Programming Languages.