Why isn't number of loops included in the EMF equation?
It is there, where you find it depends on how you define the flux. If you consider \$\phi\$ to be the flux through a single loop, then the definition of the EMF must be N times the single loop flux. If you define \$\phi\$ to be the flux from all loops, you've already accounted for N in computing the total flux and it doesn't show up in the EMF definition. In both cases, you get the same answer.

Mathematically, this could be written as (where \$\phi\$ is the single loop flux and \$\psi\$ is the total flux):

\begin{gather}
\frac{d \psi}{dt} = \frac{d (N \phi)}{dt} = N \frac{d \phi}{dt} = -\textrm{EMF}
\end{gather}