It sure makes for more dramatic price graphs.

Because market participants (i.e. brokers) need to 'mark to market'. That is, they need to transfer the net of their gains and losses to counter-parties. This occurs after the market close. To have continuously trading markets would require changing the supporting systems and regulations that support this.

Surely thats a regulation thing, not an actual desire by the market.

That just shifts the question around. Why, as king, would you want to make sure that there's a period every day when no one is supposed to trade financial instruments?

Because the king doesn't want to take the responsiblity of overlooking the transactions everyday: just when he feels like it.

How does the one relate to the other?