Consider this definition of an outer measure.
$\phi(E) = \inf \{\sum_{i = 0}^\infty p(A_i) : E \subseteq \cup_{i = 0}^\infty A_i \}$
where $A_i$ is a set of intervals which covers $E$. The problem is that this definition seems to be purely formal and impossible to use in practice. How does one COMPUTE something with this definition of an outer measure?
This is a principle that happens a lot in mathematics. We want to describe a heuristic idea in formal terms. The first step is to come up with a definition that matches our intuition, which is what you presented here. Then we can deduce properties of the definition. When enough properties are deduced, we might be able to actually calculate things with it.
In the given example, you do not want to use the definition to directly calculate some measure, that is just horribly ugly! What you want to do is use theorems about this measure. We might find that the measure equals some integral that we can just calculate with some calculus.
As an analogy, in the case you have some background in analysis of limits. When you start out learning about limits, you will most likely be asked to compute limits directly from the $\varepsilon,\delta$ definition. You then notice that this is not much fun. Later on you should get some theorems that characterize continuous functions. The l'Hopital rule is also a beauty in this area. You then notice that calculating limits is only as hard as you make it yourself.