My dad works at the OCTA (Orange County Transportation Authority) so I know a lot about the subject of freeways.
SO CAL's preference of the automobile came in large part because of the resentment toward the Southern Pacific Railroad's tight control over the region's commerce. This resentment was voiced out by anti-Southern Pacific Railroad politician named Hiram Johnson, who in the election of 1910 traveled the entire state by car, by no means an easy feat in those days. The automobile was increasingly seen as a symbol of clean, progressive government, as opposed to the train which was associated with monopoly and the robber barons (Rockafeller, Morgan, Carnegie, etc) of the late 19th century. That's probably the biggest POD there. You'd have to somehow make the Southern Pacific Railroad less monopolistic so it never catches that stigma, and you'd also have to do away with Hiram Johnson somehow.
I think the reason why East Coast cities are more compact was because those cities were founded and developed earlier, before more modern infastructural practices were discovered. LA came to be what it was because California experienced a massive influx of people who had come from the East Coast searching for land and opportunity, and thus more personal space, resulting in a more spread out population. Still, LA sprawled more than the norm for several reasons.
During WWII, LA grew into a vital defense port. The existing roads and railines suffered from bottlenecks because of the staggering amount of war material that was going through from the interior of the US. City planners recognized a more efficient transportation system was needed in order to transfer goods to the ports faster, so another series of much larger roads were constructed, which were basically the first freeways in LA. Of course, in the 1950's came the plan for an Interstate highway system, and its large defense industry and rapidly growing population made LA the ideal place to put more freeways.
One of the reasons why there is so much congestions in the freeways today is because that only 60% of all the planned routes made in the 1950's were ever completed. It is true that some of the routes were geographically improbable, such as the planned route that would go through the San Gabriel mountains, but others were not completed because of clashes with the existing communities for reasons that I consider quite petty.
For example, the 710 freeway suddenly cuts off at Alhambra. Had it been completed, it would have been a continuous route between Long Beach and Pasadena. Instead, you would have to travel from the 710, then go west on the 60 freeway to the East LA Interchange, which is the eastern edge of downtown LA, and then get on the 101 for a few miles before changing to the 2 freeway, which was constructed in the 1920's, and then you'll find yourself in Pasadena. You'd think it would be more convenient just to finish the 710 right? However, the residents of South Pasadena believed that connecting the 710 freeway to Pasadena would destroy several old historic neighborhoods made in the 1930's and that freeway noise would reduce the quality of life in the houses next to the freeways.
Also, it took until 1993 to finish the construction of the 105 freeway, which is the one that leads directly to Los Angeles International airport. Before the 105 was completed, commuters had to take a long detour by taking the 10 freeway and then going south on the 405, all because of the interests of the residents. Its because of the freeways that suddenly cut off and because of bottlenecks in the system that bumper to bumper traffic was a result.
The best soultion to the problem would not be to eliminate the freeway system all together; traffic would be even worse than it is today (if that's even possible), but rather that all the freeways of the 1954 plan were completed. Also, magically doing away with the post-Cold War recession where LA's defense industry was no longer necessary, illegal immigration and California's budget deficit would also help.
If somehow all the planned freeways in LA were completed, it would mean that there would just be less traffic.
As for LA being a sprawl hell, I suppose one just gets used to it. New York, though, that is hell.