Aside from bragging rights, why put up the tallest building in LA?

That would be Korean Air's 73-story hotel and office building that will replace the Wilshire Grand Hotel. When completed in 2017, it's supposed to be the tallest building west of the Mississippi. This was not the original idea: The Korean Air project, first announced four years ago, was going to be two smaller towers. Then stuff happened - a struggling economy along with a less-than-desired incentive package coming from City Hall - and so they decided to go with the one big tower. For Korean Air, it's an obvious (if very expensive) way of becoming an L.A. icon. The skyscraper will be cool to look at,of course, and it'll enhance the downtown skyline, but does it make sense? As an economic matter, big new office towers are iffy. When a new building goes up, at least some tenants in older, nearby buildings move in (despite often higher rents). But the local economy is enhanced only if the vacated space gets filled - and at a time when businesses are looking to downsize, not expand, that might be unrealistic. Besides, who knows what the economy might look like by 2017. Downtown's office vacancy rate is already hovering around 17 percent. Here's a summation of pros and cons of building tall from a piece in World Architecture News:

Efficiently-designed tall buildings utilize less materials for enclosure per unit of usable floor space, a smaller surface area for heat loss/gain, a natural energy share between floors and provide the potential for harvesting solar and wind energy at height. On the other hand there are disadvantages with building tall that offset, and may even negate, the benefits of concentrating people together in taller buildings. Smaller floor areas may limit people's access to natural light, views and ventilation. Growing taller requires more materials and primary structural systems, which may affect the overall sustainability equation. The general concept of 'vertical' being more sustainable than 'horizontal' may be true, especially when the larger-scale urban scenario is considered, but the myriad factors that contribute to this scenario should be better investigated.

The negative view of super-tall buildings goes back to the 1950s, as Edward Glaeser notes in his insightful 2011 Atantic piece about skyscrapers:

During the 1950s and '60s, both public and private projects ran into growing resistance from grassroots organizers like Jane Jacobs, who were becoming adept at mounting opposition to large-scale development. In 1961, Jacobs published her masterpiece, The Death and Life of Great American Cities, which investigates and celebrates the pedestrian world of mid-20th-century New York. She argued that mixed-use zoning fostered street life, the essence of city living. But Jacobs liked protecting old buildings because of a confused piece of economic reasoning. She thought that preserving older, shorter structures would somehow keep prices affordable for budding entrepreneurs. That's not how supply and demand works. Protecting an older one-story building instead of replacing it with a 40-story building does not preserve affordability. Indeed, opposing new building is the surest way to make a popular area unaffordable. An increase in the supply of houses, or anything else, almost always drives prices down, while restricting the supply of real estate keeps prices high.