Potential for a Playoff

Colleges have organized themselves into conferences with a few teams (Notre Dame most notably) playing as independents. No NCAA committee ever assigned teams to conferences. In fact, several conferences, such as the Big Ten, existed before the NCAA. Every few years, some schools jump to different conferences. A school does not need the permission of the NCAA to change conferences. Nor did an NCAA committee rearrange the conferences to fit some central plan.
Each conference decides the rules for scheduling its league games. This creates variety: the SEC, split into East and West Divisions, decrees that each team play every other team in its division and three teams from the opposite division. Big Ten teams also play eight conference games each year but are not split into divisions. Each Pac-10 school plays every other school each season. In this regard, football is like basketball and baseball for the regular season.
Each conference determines its champion as it sees fit. The SEC, Big 12, and other conferences with 12 members hold a playoff between the division winners. Conferences without a championship game rank the teams according to their records in conference games.
Each school makes its own non-conference schedule. As a result, some teams play difficult inter-conference games while others play a "cupcake" slate that may even include one or two teams from a lower NCAA division.
The NCAA once negotiated the regular season television contract(s) for all its members. However, some large universities formed the College Football Association (CFA) in 1981 to initiate legal action to break the NCAA's monopoly on TV broadcasts. The resulting court ruling freed conferences and individual universities to enter into their own TV contracts.
Each conference hires its own officials. And while they all follow the NCAA rules, they are independent when it comes to questions like when to implement instant replay and what system to use. The disparity between conferences was never more apparent than at the end of the Oklahoma-Oregon game in 2006 when the Pac-10 officials blatantly miscalled Oregon as recovering an onsides kick at the end of the game and the replay official in the booth upheld the call. It turned out that the Pac-10 was using a cheap system that did not provide the replay official with all the angles that home viewers were presented.
For 75 years, post-season play was chaotic. Local organizers created "bowl games" that invited whatever teams the bowl committee wished. Some conferences, such as the Big Ten during the 1920s and 1930s, refused to allow their members to participate in post-season contests or decreed that only the champion could play in a bowl. Others, such as the SEC, were delighted to provide bowl teams. Over time, conferences entered into contracts with bowls that preset the conference champion as one of the bowl participants each year. Starting in 1946, the Rose Bowl guaranteed both its spots to the Big Ten and Pacific Coast champs.
The NCAA has never set up a competition to determine an official champion in Division I-A football – the only one of the organization's 89 sports for which this is true. However, the concept of a "national champion" is over 100 years old. The phrase was applied to teams that finished atop national polls such as the one the AP has sponsored since 1936 or mathematical systems developed by individuals (such as Billingsley and Dunkel). Until the late 1960s, the AP conducted its final poll at the end of the regular season so that bowl results did not affect the determination of the "national champion."
In 1992, five major conferences joined with five bowls to form the Bowl Coalition in an attempt to provide more structure for post-season play. Ideally, the system was designed to create matchups between the #1 and #2 teams as many years as possible.
In 1995, the Bowl Coalition was replaced by the Bowl Alliance with a similar goal of providing the best matchups of top teams including, as often as possible, #1 playing #2. However, the Alliance, like the Coalition, suffered from the refusal of the Big Ten, Pac-10, and Rose Bowl to join.
The Bowl Championship Series was formed prior to the 1998 season and still controls the "top" of post-season play to this day, although its rules have changed several times along the way.
Bowls that have not been part of the Coalition, Alliance, or BCS have entered into agreements with individual conferences to provide the teams. And all the bowls have solicited corporate sponsors and negotiated TV contracts to enable them to pay as much money as possible to the participating teams.
The upshot of the lack of central organization of post-season play is that, in most years, there is no clearcut, universally-recognized championship team.

Part II