I'm not quite following the article. Why can't people build a duplex like that today? Which part of it is illegal? I think it has something to do with a zoning law, but I'm not very familiar with the concept. (I live in Tokyo.)
Zoning restrictions are far more restrictive in the United States than in a city like Tokyo, where the government has largely only enacted laws preventing specific cases that would be considered very harmful (opening a heavy industrial businesses in a residential neighborhood for instance).
In most of the US most land in smaller cities are zoned for single family housing only. This often means you can only build a house for one family (no duplexes) with arbitrary restrictions on a variety of other things (minimum lot sizes, maximum house sizes relative to lot size, required setbacks from property lines to the house, etc).
In the event you are able to build a du/triplex it's rare you'd be able to convert any part of it for business use unless the land was already zoned for multi-use, where they allow mixing of residential and commercial uses.
In order for a public transit system to be convenient you need a LOT of density. You also need speed. The two goals are fundamentally at odds with each other. That’s why a lot of people prefer cars. No one likes traffic or emissions, and cars are way more likely to kill you, but damn are cars convenient even in urban environments.
Any plan like this can have all these numbers talking about how much space could be freed up but they need to address this fundamental problem, and this article failed to.
Now what interesting is the rise of self driving cars. I’ve often see paid parking lots and think within 20-30 years they will be out of biz. A few large operators will emerge and park their cars overnight at some owned large lot far out of the city to recharge, maintain, etc, and there won’t be much need anymore. So that could be a path to what author is talking about, long term. Of course does nothing for parking lot owners who just hold onto the property speculating...
Changing LA's car mentality isn't going to happen overnight but it has to start somewhere.