It’s not really what LA did. LA built suburbs, single-family homes, and no mixed-use development and it was all supported and serviced by auto-only transit. That’s why they have a traffic problem. To see that this is the case you can look to many cities in Europe and how they achieved adequate results without building skyscrapers. These successful cities built single family homes but also apartments, condos, and other living arrangements while also injecting grocery stores, shops, offices, parks, and other amenities into the city and neighborhoods.
LA limited housing density via multiple policies (including a residential height limit) [0].
When I think of high density cities with low transportation problems relative to the number of residents, I think of Asia where there are not building height limits or setback laws.
I think of things on a spectrum where Asia is one end of the bad spectrum (too dense), and then LA or Houston is going to be on the other end of the spectrum. A city like Amsterdam is in the sweet spot where you have all the benefits of density and you can still have a single family house or an apartment, access to good transit and locally grown food from nearby farmers, and offices and coffee shops within walking and biking distance. They're more resilient too because you're not as reliant on fossil fuels for heating or cooling or construction, you can do maintenance on your own home (most likely) and can do retrofits for new technology, to name a few.
I think skyscrapers are an anti-pattern (though they're better than suburbs of course) because the are oppressive, block the sky, create artificially high density, and don't have features like porches where you can say high to your neighbors. You can't just walk out your front door. If there's a fire? Screwed. If you need something fixed? You depend on specialized workers (even more so than a house). Etc. They're a little anti-social. You also don't tend to have any meaningful outdoor space. I think somewhere like Amsterdam (and there are many, many other examples) is a better model. You want diversity in your buildings and living arrangements too. You want to be able to walk out your front door and down the block to a coffee shop without any barriers (car, or elevator). You want to see your neighbors and their kids. You want to be able to do work on your dwelling that you control.
Now I'm not saying that living in a skyscraper is like some sort of dystopia (though I think they look dystopian in a different way than suburbs do), but then again neither are the suburbs really. So I don't think I can honestly rail against one (except on energy expenditure) and not the other since to me they are both bad compromises whereas medium density, mixed-use walkable towns and neighborhoods with height limits probably around 3-5 stories give you everything you could ever want and more. They blow everything else out of the water.
