(Just to keep up with US population growth Los Angeles County needs to build over 30k homes every year.)
While a few notable buildings opened up in downtown during that 2013-2016 time period (i.e., 8th and Grand, One Santa Fe in the Arts District, the Whole Foods Lofts, the Last Italian Fortress), most of the units in downtown have only recently come onto the market, i.e., in 2017 and 2018.
Some of the biggest developments in the Arts District and South Park are still under construction, and the biggest developments only broke ground this summer.
https://la.curbed.com/2017/4/13/15288974/la-metro-housing-co...
LA has no single center of gravity. We have high rises in Downtown, along Wilshire in Korea Town, in MidCity/Beverly Center, Beverly Hills, Century City, Culver City. LA has hundreds of multi-unit apartment and mixed use buildings. Between downtown and the beach, most of the area is zoned for multi-unit residential with multi-unit buildings scattered between single-family blocks. Only a few neighborhoods are entirely single-family homes.
Unlike Texas, Oklahoma, or Kansas, we have these things called "earthquakes" that can cause significant amounts of damage and death and our building codes are more rigorous to minimize those risks. This also makes it more expensive to build housing--but that's a good thing. You don't want a ton of people living in shoddy houses that will collapse and kill them.