The inclusion of non-Champions started ironically around the time that they started calling it the "Champions League" rather than the European Cup which had existed very successfully since the 50s as a straight knockout competition between the winners of the domestic leagues around Europe the previous season. However, chairmen and owners of the more brand-orientated clubs, led by Silvio Berlusconi of Milan and whoever the Real Madrid owner was then, decided that it wasn't generating enough money for them. They reasoned that Milan vs Juventus was a bigger TV pull than FC Basle vs Rosenborg, and so, I think, basically threatened UEFA until they got their way and the league format was introduced, with a greater number of games guaranteed with more clubs from the major leagues of Italy, Spain, England and Germany. It's all fallen into place for them where some clubs are as good as assured of qualification for the competition each season, generating a huge amount of money for them and ensuring the most exciting players will only consider joining clubs who will provide them with the hallowed Champions League games. This creates and maintains a horrible financial and achievement hierarchy to the point where the odds of the top 3 this season not being Chelsea, Man Utd and Arsenal were extemely long and coming fourth over fifth is more important than first over second. It's very unhealthy for the game currently and for the future in terms of spectator interest.
Apologies if that was a rant/lecture.