Of course there are, but look at PR systems, where each party represents a much smaller segment of the population than one of the big two parties. As a result, many more parties get elected, and many more viewpoints have to be taken into account in order to do anything in government.
Fund-raising (wealth and popularity of a candidate would have even MORE effect if political parties were lost), organization and practicality (especially with the primary system), decline in participation in the political system, increased governmental influence (as parties are private entities, the government would completely control all elections, instead of the semi-private primary system), increased regionalism and pork (historically, candidates in non-partisan systems have organized by region, to bring as many resources to that region as possible, instead of organizing in other ways), increased vote splitting, letting less-popular candidates take an election.
You think that they would? Most people are not engaged enough in the process to do so, and thus TV advertisements and the media's influence on the political process would increase.