It made more sense to place Richie as Ash's main rival in that opening because he actually got to bettle him in the league. Gary, while he was Ash's 'official' rival, didn't even get to face him until the end of the Orange league, by which time he had adopted his "I'm a nice guy now! =D" attitude.
Ash has really poor rivals in my opinion. I mean, he doesn't even really have one now... I guess Masamune, but he's kinda... blech. And Ash only saw the guy like twice. I would really like it if he had a rival that forced him to his limits, was as frequent or more frequent with his/her appearances as Drew is, and had some under-represented pokemon in their team. Not another shoulder-sitting Pikachu and similar clothing to Ash. *coughRichiecough*