LA (the city) is relatively dense (medium-high density) compared to its cursory reputation of being low density.
but public transit here is imperfect, to be sure. it's good if you live near a train line, and not so good if you have to depend only on buses. LA metro and LADOT are trying to change that, but it's a frustratingly slow process. micro-mobility options (e-scooters, e-bikes, car share, etc.) help.
Density of city limits would maybe be more appropriate when talking about subway service or LA's light rail. So that'd be about 8,092/sq mi for LA and 28,491/sq mi for NYC. Maybe MSA would make sense for things like commuter rail, which runs something like every 20 or 30 minutes (hourly on weekends) for Metro North.
And "induced demand" is a misnomer. Existing congestion suppresses existing demand, which comes back when you relieve some of it. You need to find better ways to satisfy the demand, not find ways to further suppress it.
The best way to do that is to increase density, because that both makes mass transit more viable on its own terms (more frequent trains and they're still full) and decreases the number of miles people have to travel because things are close together.
It would be idiotic to create an LA train system designed to handle only the amount of people that will busing it within the first year.
> It would be idiotic to create an LA train system designed to handle only the amount of people that will busing it within the first year.
Of course you do. Trains replace buses in the places with enough density to justify them. You don't build a train in a place that would only see it half full, you just run a bus there which holds half as many people.
The problem is most of these places can't even fill a bus every ten minutes because everything is so spread out. You need more taller buildings first.
[1]https://www.citylab.com/transportation/2018/01/why-its-so-ex...
To fill the same subway cars in LA would require intervals more than 25 times longer, i.e. more than two hours instead of every five minutes, and then it's garbage and nobody wants to use it. Or, in practice, you only run mass transit along the most popular routes and then the majority of people can't use it because it doesn't go where they're going.
Making it less convenient to drive doesn't really fix that, all it does is make more people miserable, because you make driving worse where no viable alternative to driving is available. The only real way to fix it is to reduce sprawl so that you have more density over less area -- and that's only possible in the long-term, so in the short-term LA is pretty screwed for traffic. But that's no excuse to not be working on the long-term solution.