Why do some authors not include summation in the $\pi$-Calculus?
To answer this question, it's best to reflect on the meaning of sums in process calculi. Essentially sums express a lack of knowledge. The process $P + Q$ means something along the lines of "either $P$ or $Q$ is active, but I have absolutely no information which". Note that this is related to, but different from a probabilistic sum like
$P +_{0.5} Q$ which also expresses uncertainty about which process is active, but quantifies the uncertainty by stating that both outcomes are equally likely. So $P+Q$ expresses less information than $P +_{0.5} Q$.

A specific case of using sums to express uncertainty is the input process

$$
   x(v).P
$$

Cleary an process waiting on an input on channel $x$ is uncertain what input will be received, for otherwise there would not be a need to input something. Hence
input can be seen as a sum over all possible inputs, e.g. if we expect to get a natural $n$, then $
   x(v).P
$ really is the sum:

$$
   \Sigma_{n \in \mathbb{N}} xn.P\{n/v\}
$$

Here $xn.P$ is the process that inputs the number $n$ (seen as a constant) on $x$ and becomes $P$.

With this understanding of sums as an expression of uncertainty, the question
whether to include sums, and what kind of sum 
 depends what you use the $\pi$-calculus for. There are two main uses.

If you use it as an idealised programming language, then you don't need sums other than the input prefix  $x(v).P$  (and possibly its replicated variant). Indeed what computation would $P+Q$ express? 

If you use it to specify program behaviour, then you typically don't want to specify everything and instead express uncertainty by using sums of processes, e.g. $P + Q$. Typically you don't know exactly what the environment of a process is going to do, and use non-determinism to formalise this lack of knowledge.