Answer
The reaction (Consider HA a strong acid):
$HA (aq) + H_2O (l) --\gt A^-(aq) + H_3O^+(aq)$
Is not treated as equilibria because, it only happens in one direction (Forward). Normally, the $A^-$ and $H_3O^+$ don't react, so there is no reverse reaction, therefore, the reaction doesn't have a equilibrium.
Work Step by Step
Equilibria ionizations have 2 reactions at the same time, for example:
$N{H_4}^+(aq) + H_2O(l) \lt--\gt NH_3(aq) + H_3O^+$.
- In this case, since the arrow is pointing to both sides, the $NH_3$ is reacting with the hydronium ion, and, at the same time, the $NH_4^+$ is reacting with the water. Therefore, this is a equilibria.