Most cameras on a rocket launch are there for a sound engineering reason.
They look down at the engines of the rocket, or up to the second stage, or out to the solar panels, or down inside the propellant tanks. The reason they look at these things is to evaluate performance, observe if anything goes wrong, and to serve as a tool in analyzing what went wrong in the event of a mishap.
For example, this nice video from a Shuttle SRB looking up at the shuttle body during separation:
However, in many the years of rocketry the horizon has proven to be exceptionally predictable. Not once has it suffered burn-through or break-up, and it does not yield a bit even to the most strenuous Max-q forces. Thus the engineers have little interest in a camera that shows nothing but horizon. They are quite content with the peripheral view of the horizon from the down or up-facing cameras.
One might want a side-view for PR purposes, but think about it. What will such a view show? A noise, some vibration, and a rapid elevator ride. Very similar to the view out of an airplane's window, but minus the context. We get the same view, but with much more, from the ground-facing cameras. Now a video from inside looking out, that has some PR potential, because it provides the context to give the view some real meaning. Like this view on the New Shepard launch.