Many European cities actually have very wide streets—they just choose to cede space for bikes, trams, buses, and wider sidewalks, instead of dedicating 100% of the streets to single-occupancy cars and car storage like we do.
The difference in density and sprawl between pre-car and post-car cities is staggering, and is not about the width of streets. You can't get around Los Angeles without driving on freeways.
With investment in public transit (i.e. approximately rebuilding the original streetcar network and building out the existing Metro system) and a high-quality protected bike lane network, LA could be truly amazing.