From the AD&D 1e DMG, page 106:
It is an assumption that high-level player characters with strongholds "will desire some dungeon mazes" beneath them. This is not referring to something like a castle dungeon one might find in the real world, but the "dungeon mazes" characteristic of D&D - specifically early D&D. We're talking dungeons like those you might generate using the tables in APPENDIX A - something weird like this:
It seems a bold claim to make that player characters simply will desire this sort of complex beneath their stronghold. Can the fighter not fit their men-at-arms' barracks and armory in the castle proper? Can the cleric not accommodate their shrine and altar in the above ground portion of their place of worship? Can the magic-user not find room for their laboratory in one of the many levels of their tower? Why would a character "desire" this?
APPENDIX I: DUNGEON DRESSING provides some examples of rooms which might be found in a dungeon:
Surely any of these could just as easily be included in the structure above ground, no? Is it somehow more convenient to construct these rooms below ground?
Gygax helpfully provides the cubic volume of rock that can be mined in an 8-hour period by different demihuman/humanoid races and monsters:
And, of course, since this is AD&D there is detailed guidance for determining the productivity of slave labor and number/quality of armed guards needed to ensure maximum productivity and keep the slaves in line:
There isn't much to suggest that underground construction is cheaper or faster than above ground construction, save this bit under CONSTRUCTION TIME:
An excavated subterranean area is, after all, the crudest form of a "room", I suppose. If properly excavated and supported, it may obviate the need for building materials like dressed stone, which in turn eliminates transportation costs. For proper "interior dungeon walls", however, one must extrapolate from the cost of above ground stone buildings:
It is also worth noting that the player character would likely want their above ground construction to be protected by walls. The more such construction one undertakes, the more area the walls will have to cover. Walls are expensive:
Underground construction, on the other hand, comes with its own walls (albeit crude ones, unless the player character wishes to spend additional money to improve them, as previously mentioned).
So maybe subterranean construction ends up being more cost efficient than above ground construction, even if not explicitly stated in the text. I'm not sure there's enough information to easily determine whether this is true, and I don't particularly care to do the accounting anyway.
As to why player characters might desire dungeon mazes beneath their strongholds, I think there's a more fun explanation.
Retired adventures, settled in their strongholds with armies, tax-paying settlements, and the occasional wandering monster to manage, now part of the established order, long for the dungeon. It's where they came of age, tested their mettle against monsters, tricks, and traps, and accumulated their power and wealth. They miss it. Deep down inside, they've always wanted one of their own. They're bored. They have money. Their mind wanders back to the dungeon.
I'm still not entirely convinced that player characters will desire to build mazelike dungeons beneath their strongholds. Maybe it would be fun to coordinate with the DM on a project like this, slowly building out your dungeon for the next generation of player characters to one day explore. Maybe this is a pastime the gamers of the late '70s enjoyed, but I don't see it happening in the play culture we're familiar with today.
Rather, what I think is more interesting is the more general assumption that high-level NPCs will build mazelike dungeons beneath their strongholds. It then follows that every fighter's castle, cleric's temple, and magic-user's tower encountered in the wilderness has a dungeon underneath it.
I'm not supposing that these NPCs are true dungeon sickos, filling their labyrinths with monsters, tricks, traps, and treasure (although it would be fun if they did - you could take the classic "a wizard did it" dungeon trope and expand to include any characters class). Rather, I imagine these dungeons would simply be subterranean expansions of the stronghold above - more armories, more chapels, more laboratories, and so on. I suppose then that the "monsters" would just be men-at-arms and other guards, and tricks and traps might be in place to guard treasures secured therein against possible invasion and looting.
What I find most interesting about this is it answers a question I grappled with back when I wrote about "totally deserted" castles: are these supposed to be dungeons or not? Now, the answer is clear: Yes, totally deserted castles do contain dungeons underneath, because all high-level characters will build dungeons beneath their strongholds.
While inhabited "castles" (meaning strongholds in general) will have dungeons which are more or less extensions of the above ground construction in terms of purpose and contents, deserted castles will be weirder, proper dungeons. Their layout and dressing will be consistent with their original purpose and occupants, but the whole will be filtered through time and ruination. The armories contain crumbling weapon racks and tattered coat of arms, and are now home to rust monsters who have eaten all of the weapons and armor once stored there. The chapels contain defiled altars, fetid pools of unholy water, and perverted holy symbols, and are haunted by undead who draw power from the desecration. The laboratories contain wilted herbs and beakers and flasks in disarray, boiling over with alchemical oozes.
This presents adventurers as not just the young upstarts who foray into dungeons, clear them out, and abscond with their treasure, but also as the old retirees with a late-in-life hobby, who in their hubris (or by their own design) perpetuate the ruination which they once exploited - by carving out the labyrinths monsters will one day inhabit, placing the tricks and traps that will deter future looters, and hiding their accumulated wealth behind secret doors and shifting walls for their successors to discover, accumulate, and eventually begin the cycle anew.
That other category of deserted castle - "deserted (monster therein)" - also presents a more interesting scenario in this light. The castle is not just a monster lair with a unique skin - rather, the dragon, orc warband, or will-o-wisp which now inhabits the castle is an additional (and deadly) obstacle which must be overcome before the riches of the dungeon beneath can be plundered.
While dungeons in AD&D are adventure sites which are "balanced" according to dungeon level such that they are a fitting challenge for low-level characters at the start and get progressively more dangerous as the characters delve deeper within, deserted castles which contain a monster on the surface are stocked using the wilderness encounter tables, which are considerably less "balanced" and more dangerous for low-level characters. The low-level adventurers who wish to plunder the level-appropriate dungeons beneath such a deserted castle are unlikely to be able to face the monsters inhabiting the surface ruins head on. This opens the door to creative solutions such as deception, parley, or the discovery of a secret means of ingress.