Why is $\Sigma_a^0$ is defined as countable unions of elements just from $\Pi_{a_i}^0$ for $a_i<a$ and not also from $\Sigma_{a_i}^0$?

Question

Topic: Borel Hierachy

$\Sigma_a^0$(definition): Countable unions of elements from $\Pi_{a_i}^0$ for a sequence $(a_i)$ such that $a_i<a$.

Due to the above definition, in general, we don't have $\Sigma_a^0 \supseteq \Sigma_b^0$ for $a\geq b$. This seems very unnatural as the motivation I was given for the Borel hierarchy is to construct Borel sets step by step.

Indeed for nice topological spaces the inclusion holds but the question remains for spaces in general: Why is it done this way and not in one that makes that inclusion hold for all topological spaces?