I live in LA and have several friends who bike as their primary mode of transport. It's not easy. You have to be alert at all times. Outside of that, though, it's surprisingly viable. With a bike and Metro, you can get most anywhere in a reasonable amount of time.
So? Unless you are ethically opposed to anything with four wheels, it's a cost/benefit tradeoff. If a car is X hassle and Y money, but moving to LA saves you 2X hassle and 2Y money...