In Tite Kubo's Bleach (the manga), what exactly was the Soul King? What was its function within the metaphysical arrangement of the Bleach world?

The Bleach wikia page says:

The Soul King is the king of Soul Society

Not really - it didn't rule soul society. Also, don't you have to be a person to be a king? Also, the same page says:

The Soul King is not involved in governing Soul Society, having given the full control of its government to the Central 46

It's not clear that the Soul King actually has actually "given" anything to anybody. Was it a proper king earlier, then? And is it an eternal entity, or some guy (well, spirit) which closed itself away?

The Soul King's sole purpose is to regulate the flow of souls into and out of Soul Society and keep the flow stable.

What does that mean? Is it controlling death and birth rates in the real world?

Without the Soul King, the balance is lost and everything that is linked to Soul Society or made in it, as well as the Dangai, Hueco Mundo and the Human World will fall apart

That's a rather vacuous statement, considering how strongly Aizen and Yhwach feel about the Soul King.

So what's the deal with that thing?