Looking at examples in AlexP answer I started to like the idea, and here is reasons why.
In contrary to your desire to push poor people in dark corners of such building, it provides more window space, and day light as resilt, for the same amount of volume(apartments) and materials used. For longer period of time if such buildings are next to each other.
- turns out it is the case for small ones
Volume of pyramid is 1/3 of base area multiplied by heigth, for a rectangular it just base multillied by height. So for the same efficiency pyramid building has to be 3 times higher.
Surface area, sides of pyramid 1/2 × Perimeter × [Slant Length], Slant Length is more than height so, surface area of pyramid is at least 1.5 times more.
If you build it more like egyptian pyramids, not just a smooth slope, like sky scraper faces, but step wise floors, then the building is more safe in cases of emergency, you can have ladders on outer side of the building. And even if there is no access to internal or external emergency exits, you can make few floors martial arts style, not being one. And then leave building trough standart emergency exits.
- in that sense none of the examples from AlexP is good, maaaybe via 57 west to some extent, buut yeah typical pyramid thing would be better.
Building could have balcony or patio type things next to apartment, public or private. Privacy would not be so great there, but hey more like public beach thing, almost nothing surprises people those days.
- maybe even some green roads on exterior of the building to walk, eh? Why not. Such buildigs probably can expand city surface accessible for humans to walk two times or more(I mean expand it by the footprint of buildings, add it to the accessible surface)
The side of a building being stepwise, makes it harder to trow things 200 floors down, it most likely lands 5 floors below or something. So open exit on side of the building does not create that much more danger to people and vehicles on ground level. (Not quite, but yeah there is something in that)
A building process of such building by itself can be more safe and easier. Maybe even faster because of that. I do disagre with someones statement that such building is harder to build, yes maybe for examples like on pictures there are some custom solitions, but for typical pyramid, that step side design, it barely any different from a typical not sky scraper building. You will have the same supporting elements from top to bottom, so it even more unified and suitable for massproduction.
The building is more stable on a ground, that is for sure. However side wind will act maybe, not necessarly, a bit more on the building, but with lesser effects at apartment. So probably basement has to be bit stronger.
It is good for places with cold climate.(subjective)
Floors can be insulated and separated from each other, in some sense, sound proofing may be easier. Not just your typical soundproofing, which isn't an easy task in many constructions because of supporting beams under load/compression going basically from top to bottom and if not impossible but then it not an easy task to stop them to conduct sounds. With a pyramid it basically rectangulars smaller and smaller on top of each other, and between them you can put a vibrations dumping sandwich of your dreams. Metall working factory on top floor? No problem, you will not hear a thing from there.
Such unbinding of floors also means each can have its own layout, purpose and functions - so more flexibility for volume planning, more customisations possible. It will bring its own limitations as wel, but still. There is a pair of building in NYC(if I recall correctly) which are build over a road, idea was to use space above the roads in a usefull way - smell was a problem (Elon save us faster) but also noise is a problem as I heard.
A high building is 800 meters, so for the same footprint efficiciency pyramid has to be 2.4 km high. And that brings atmosphere pressure problem. And higher than that, or even at that height it will strike out some good stuff I mention before. So it limits the size of it, if benefits are to be keept.
- not a such big limitation really, 1km by 1km base
Surface area of one building indeed is bugger, but compared to many rectangular buildings with the same footprint, with roads and stuff between them, it may(will) be less.
but on the other hand it not necesarly bad, as there are multiple uses for "extra" internal volume, including appartments for people who prefer not to see the fusion reactor in the sky.
Internal volume can be used for storages, shops, datacenters, trash recycling, waste water cleaning, drinkable water processing, energy production(modular mini nuclear reactor as an example). So yeah, arcology on the scale of a building. Which may be more energy efficient, require less city communications for the building. Some production of some goods locally is possible, starting from simple handmade soap to more industrial things(this needs an explanation, but out of scope, helpfull things in this direction are already in development) eliminating some logictic transportation chains/needs.
rectangular vs pyramids
Things depend on what is the percentage of internal space to which do you have practical and good use, per appartment. This percentage will define maximum height of the building, for a given slope. If you use 100 percent of it for cows, chickes, pigs, poor people, horses, production facilities, recycling waste processing, parkings, etc then you all in for pyramids, no question asked.
- ability to hide parking deep inside alone can be one of the reasons, as there is no way to hide the ugliness of parking buildings otherwise.
If there is not so much use for that space, and you need to have less of it, then it limits height of the building, and as we have seen it should be 3 times of rectangular one, so if it is less than that then footprint is used less effective.
So if it more like spaceship-building, onnself sufficiency side of things then it quite futuristic approach and may have place in the future as main design.
If it is 50/50 volume, and apartment surface layer is 25m deep(apartments plust that step thing), slope 45 degree, then size of the building is about 70×70 meters base and 35 meter high, soo will be in some sense less effective land use in area where buildings are 12 meters and higher. (Numbers not exact, to lazy calculate it properly, so I use only base surface as reference)
If proportion is 10/90 (external/internal) then 160×160×80 meters, not a sky scraper, but for areas where typical rectangular building is 30m high. (Would be okay for my city)
If proportion is 1/99 golden percent, or spaceship arcology building then 500×500×250 for areas witn typical buildings 80m heigh. Not a sky scraper. (More than enough for my area)
Soo use of internal space is a limiting factor for real life, and if you find a use for it, as an example you can have full in house food production and other types of production there and then it will require some surface/internal volume there, it will cost quite an energy poduction so only nuclear option, because even golden percent is not enough to bring it to skyscraper territory.
Soo rectangular sticks seems more land efficient, and sells better, otherwise pyramids are good.
So the answer is
What do you need is a use for internal volume beyond rich poor proportions. Or do not care about land, there are one floor cities, so why not.