In quantities such as speed where the derived (SI) unit is m/s, why do we pronounce it and interpret it as meters per second? My guess is that 1 m is associated with 1 second. Similarly, 5 m/s is pronounced and interpreted as 5 meters per second, because 5 meters are associated with 1 second. I am not sure whether this view is naive.
It is an instantaneous value. The speed, in m/s (or any other unit) is:
where $s$ is distance/displacement. If speed is constant, it really doesn't matter: an object moving at 5 m/s will cover 5 m in every second.
It will be very different if the speed varies. Imagine a dropping stone, subject to a 10m/s/s acceleration. At 1 s, the instantaneous speed is 10 m/s, but that speed occurs for exactly zero time.