Why is the notation for reactions not explicit?
The reaction, described in the form given in the original question, i.e.

$$\ce{C + O2 -&gt; CO2}$$

simply conveys that each formula unit of carbon reacts with one formula unit of oxygen to yield one formula unit of carbon dioxyde. As such, for example, useful to balance how many grams of carbon may be burnt with $\pu{22.7 L}$ of oxygen.  As such, yes indeed, it is a limited representation.  In an analogy, it is like book keeping; (within reason) is does not matter how you paid at a garage (cash, debit or credit) to get your car back -- but to satisfy both sides, it has to be balanced.

This view contrasts with many organic reaction equations as reaction mechanisms which are intentionally drawn with further detail like this:



(source)

Here, the how is important, and consequently outlined with more attention.  As if you would need to explain an apprentice how the teeth of a gear have to be adjusted in face, pitch, flank, etc. to transmit the force from the engine to the wheels.