Yeah, there was a lot of talk about them not having that part of the logo on Ruby and Sapphire when they came out. (I believe they were still on the GSC games, though.) If I remember right, the discussion basically ended with us agreeing it had something to do with them trying to update their image.
Personally, I think that part of it may have been that in the anime, Ash is not on a quest to "Catch 'em all," which would have created some conflict with that motto. I have no real evidence for that, but it would make some sense for that to have played a part in the decision, at least in my opinion. But as for the games not using it, I'm pretty sure it was all about their image.