Why can the number of zeros be no more than the number of delay elements in a signal flow network?
There is nothing preventing you from writing down an expression that has more zeros than poles.  In fact, a typical FIR filter may be designed as something like $$\sum_{n = -\frac{N-1}{2}}^{\frac{N-1}{2}} f(n) z^n$$
giving you a filter that's nice and symmetrical around zero delay.
The problem is, that in the physical world, $z$ is a lead operator -- it fetches samples from the future.  Since physicists stubbornly refuse to invent time machines for us, we have to make do with filters that only operate on past values of the input.
Thus, we only allow $z^{-n}$, and accept $z^0$ because we have an unspoken agreement that it means &quot;the latest sample, with just a bit of delay&quot;.