A Drill City is an entire city worth of Morlocks in the form of a giant drill, making its way through the underworld.
The culture of a Morlock Drill City is ruled by Hate Priests, and they direct the hate of all Morlocks at the Eloi (their word for any soft (aka, neutral or lawful) surface-dwelling humanoid) and away from each other, allowing their society to function.
The part of the puzzle not mentioned is how the drill cities are powered and maintained. Obviously Morlock society must be able to at least maintain these cities, or they would quickly break down from the rigors of drilling through the underdark. Who are the engineers?
In D&D 5E terms, it's obvious that the two most common form of Wizard are Conjurers and Transmuters. Morlocks have no interest in the subtle nature of divination, illusion, or enchantment, or the defensive arts of abjuration. They also do not produce many Evokers, as they prefer to kill their enemies with knives and teeth - blowing them to smithereens with a Fireball doesn't leave any bits for eating.
But Conjurers and Transmuters are useful. They are the engineering class of the Drill Cities.
Transmuters are the more common, lower caste of wizard, and they perform two functions. They take in the ore that the great drill produces and extract all the useful minerals and metals from it, siphoning them into reserves of materials. They then magically transmute these materials into useful alloys and shapes to form the machinery that allows the Drill City to function. Most of it goes into the drill face itself, as it needs constant maintenance to not be worn down to a nub. But they also make the glass cloning vats Eloi meat is grown in and the metal pipes and boilers that drive the city and move steam and waste. Morlock Transmuter Stones can be sacrificed to jump-start a cloning vat or permanently transform a captured Eloi's hands or other body parts into specialized forms (the same way insect colonies have specialized drones). The Chief Transmuter of a drill city would not try to lead or influence the Hate Priests, but he is influential enough to be immune to their machinations.
The Conjurers are a smaller caste of specialists. Only the most promising Wizard apprentices are admitted to their ranks. Their function is to summon and trap the Fire and Steam Elementals that power the drill city. They take great pleasure in torturing a Fire Elemental, repeatedly dowsing it in water to produce steam that drives the great machines. Ultimately this kills the elemental and then the Conjurers are driven to summon a new one. Fire Elementals are relatively easy to contain though, as they are surrounded at all times by water which they loathe. It is a cage to them. The Steam Elementals are far trickier to manage, as they can escape into the steam tunnels and wreak havoc, but their use is necessary to clean out the miles of pipes and vats that allow the city to grow food, move water around, and manage waste. Many "unfortunate incidents" in the Drill Cities are the result of an escaped Steam Elemental.
Despite being the Engineering class of the Drill Cities, no Morlock wizards, not even the Chief Transmuter, have Scottish accents. None of them. Anyone who breaks this rule will be drawn and quartered.