Why did we introduce the concept of oxidation number in chemistry?
Oxidation number is a deliberate approximation to make keeping track of electrons in molecules easy
You are quite right to say that oxidation number isn't &quot;true&quot;. It is clearly a simplified idea and not a perfect representation of &quot;reality&quot; whatever that is.
But there is a point to it. That point is to enable chemists to keep track of the electron count in molecules. Electron distributions may be infinitely variable in bonds but electrons are discrete and keeping count of them is important. In transition metal complexes, for example, it is important to make sure all the bonding electrons are correctly accounted for. Many transition metals can have variable oxidation states with very different properties and the (crude) approximation of where those electrons are helps us classify those differences even when the metal-ligand bonds are covalent and the electron distributions are not clear-cut or ionic.
So there is no intent to correctly represent the distribution of charge in bonds. But pretending the oxidation number is an integer helps keep track of things and is often very useful at explaining properties.