If you consider how such a quantity may have come about, you could believe that it would be most useful to the average person when making comparisons between every day occurrences involving movement.
My assumption is that the concept of speed would have arisen in an "every day" context rather than coming into being as a pure mathematical definition.
A related answer in Stack Exchange states that the concept of speed predated Galileo by a long way which supports this assumption.
For example, consider an historical era predating free access to basic education, pre-calculus, where a horse travels 10 leagues in a day, whilst another travels 6 leagues in half of a day. How might someone in some historical, compare which is fastest?
You need an averaged quantity that describes the rate at which the horse travels i.e. you would have to long it takes each horse to travel the same distance. To my (admittedly biased) mind, this leads naturally to the concept of speed but without the definition we now use without hesitation.
Obviously, we know that, in this example, one horse travels 10 L/day whereas the other travels 12 L/day, and we, without modern educations, interpret those quantities as speeds.
Therefore, I believe the concept of speed is simply a result of we humans wanting to make simple comparisons of moving objects in Nature, which has eventually been made rigorous in its meaning, and even been extended through calculus to the concept of instantaneous speed.