Why does water react with H+? As we all know, if we put $\ce{H^+}$ ions in water then water reacts with them and produces $\ce{H_3O^+}$:

$$\ce{H_2O + H^+ &lt;=&gt; H_3O^+}$$

My question is, why does water react with $\ce{H^+}$ in the first place? It doesn't have an electron, then how can the reaction occur?

And again, it's already stable and adding one more $\ce{H^+}$ will, in my understanding, destabilize it as it will have one more proton in the molecule.
Water has two lone pairs. H$^+$ is a naked nucleus with a positive charge. It is extremely reactive and would bind to any neutral molecule. Water has two lone pairs of electrons and H$^+$ binds one of them to form H$_3$O$^+$.

In absence of water it would bind other things. For example, it would bind methane to form unstable CH$_5^+$ that breaks down to CH$_3^+$ + H$_2$.