The ruler must be of God's lineage (an angel) to prevent chaos. Nonetheless a demon can serve as second in command, a notable example being Mazikeen. Charlie, as a half-human/half-angel, could serve as king, as it shown that Dromos planned to mold Charlie into becoming the king he wanted.
The King of Hell oversees the realm. He is responsible for controlling demons, ensuring damned souls get punished, and keeping the kingdom contained. He must also have his servants (demons) patrol the gates of Hell, making sure damned souls do not escape.
The first ruler of Hell was the angel Lucifer (formerly Samael), who was cast out of Heaven as punishment for rebelling against his father, God. Lucifer unwillingly ruled over Hell for billions of years, even long before there were damned souls, before deciding to abdicate his throne and leave Hell for Earth.
In Lucifer's absence, Amenadiel was forced to run Hell, a job he loathed. Amenadiel was unable to rule Hell because the demons would not take orders from anyone but their king Lucifer. Amenadiel tried numerous times to convince Lucifer to go back to Hell but was unsuccessful.
Lucifer had suggested to his mother, the Goddess of All Creation, to become the new ruler of Hell as opposed to her original plan to return to Heaven.