I chase low price to a certain point. If the routing is incompatible with my schedule, or I do not feel safe on the airline, low price is of no use to me.
That said, I disagree with the assertion that low price equals to low quality of service. The airline industry has a high barrier to entry, and thus competitions cannot arise overnight even if someone has a great idea to try. Since foreign airlines are able to out-compete US airlines both on price and service, I suspect new business models will come about to provide American customers with a choice to counter the trend toward LCCs. The principles of free market does indeed work, it's just that in the not-so-fluid airline industry, it'll take a while.