Looking at examples in AlexP answer I started to like the idea, and here are the reasons why.
In contrary to your desire to push poor people into dark corners of such buildings, it provides more window space, and daylight as result, for the same amount of volume(apartments) and materials used. For a longer period of time if such buildings are next to each other.
- turns out it is the case for small ones
The volume of a pyramid is 1/3 of the base area multiplied by height, for a rectangular it just base multiplied by the 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, the surface area of the pyramid is at least 1.5 times more.
If you build it more like Egyptian pyramids, not just a smooth slope, like skyscraper faces, but step-wise floors, then the building is safer in cases of emergency, you can have ladders on the 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 the building through standard 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.
The building could have a balcony or patio-type things next to an apartment, public or private. Privacy would not be so great there, but hey more like a public beach thing, almost nothing surprises people those days.
- maybe even some green roads on the exterior of the building to walk, eh? Why not. Such buildings probably can expand city surface accessible for humans to walk two times or more(I mean to expand it by the footprint of buildings, add it to the accessible surface)
The side of a building being stepwise makes it harder to throw 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 dangerous to people and vehicles on ground level. (Not quite, but yeah there is something in that)
A building process of such a building by itself can be safer and easier. Maybe even faster because of that. I do disagree with someone's statement that such a building is harder to build, yes maybe for examples like in pictures there are some custom solutions, but for a typical pyramid, that step side design, it barely any different from a typical, not skyscraper building. You will have the same supporting elements from top to bottom, so it is even more unified and suitable for mass production.
The building is more stable on the ground, that is for sure. However side wind will act maybe, not necessarily, a bit more on the building, but with lesser effects on the apartment. So probably the basement has to be a bit stronger.
It is good for places with cold climates. (subjective)
Floors can be insulated and separated from each other, in some sense, soundproofing 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 rectangular smaller, and smaller on top of each other, and between them, you can put a vibration dumping sandwich of your dreams. Metall working factory on the 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 customizations possible. It will bring its own limitations as well, but still. There is a pair of building in NYC(if I recall correctly) which are built over a road, idea was to use space above the roads in a useful way - the 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 efficiency 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 mentioned before. So it limits the size of it if benefits are to be kept.
- not such a big limitation really, 1km by 1km base
The 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 necessarily bad, as there are multiple uses for "extra" internal volume, including apartments for people who prefer not to see the fusion reactor in the sky.
Internal volume can be used for storage areas, shops, datacenters, trash recycling, wastewater 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 fewer 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, helpful things in this direction are already in development) eliminating some logistics transportation chains/needs.
rectangular vs pyramids
Things depend on what is the percentage of internal space to which do you have a practical and good use, per apartment. This percentage will define the maximum height of the building, for a given slope. If you use 100 percent of it for cows, chickens, pigs, poor people, horses, production facilities, recycling waste processing, parking, 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 the 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, oneself sufficiency side of things then it quite futuristic approach and may have a place in the future as the main design.
If it is 50/50 volume, and the apartment surface layer is 25m deep(apartments plus that step thing), slope 45 degrees, the size of the building is about 70×70 meters base and 35 meter high, soo will be in some sense it is a less effective land use in an area where buildings are 12 meters and higher. (Numbers not exact, too lazy to calculate it properly, so I use only the base surface as reference)
If the proportion is 10/90 (external/internal) then 160×160×80 meters, not a skyscraper, but for areas where a typical rectangular building is 30m high. (Would be okay for my city)
If the proportion is 1/99 golden percent or spaceship arcology building then 500×500×250 for areas with typical buildings 80m heigh. Not a skyscraper. (More than enough for my area)
Soo the 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 production so only nuclear option because even golden percent is not enough to bring it to skyscraper territory.
Soo rectangular sticks seem more land efficient and sell better, otherwise, pyramids are good.
So the answer is
What do you need is to find a use for internal volume, beyond rich-poor proportions. Or do not care about the land, there are one-floor cities, so why not.