Why is Demon King not leaving purgatory? Why are there no frontal battles between the Demon King and the Supreme Deity (the goddess)?

Is there a rule to prevent that?
There was a great war between the clans 3000 years before the current time in The Seven Deadly Sins. The two main clans on each side were the Demon and the Goddess clan. There indeed must have been battles between the Demon King and the Supreme Deity at that time however none of that is shown in the anime or the manga. At the end of the war, the Goddess clan basically ended up defeating the Demon Clan by sealing them away for good using the Coffin of Eternal Darkness. The seal was eventually broken partially by Hendricksen freeing the Ten Commandments and many other demons but it was not enough to revive the Demon King himself.

So basically, Demon King cannot leave the Purgatory. The Purgatory is a space between the living and the afterlife. It is similar to how Meliodas didn't move go to the afterlife and instead went to the Purgatory. So the Demon King isn't really dead but not much of a living being either. He is simply waiting for someone to revive him.