I'll admit from the start I liked it, thought it was a novel idea to perhaps even spice up the long and arduous baseball season. Now however it needs to end, because other than a few geographical rivalries which bring in big box office numbers, there's really no point to it anymore.
It is only May and some teams in both the American and National League are already done with each other for the rest of the year. How crazy is that? Or that fact that some divisional rivals won't play until late July, long after they've already played multiple teams from the other league. Additionally I also believe that the schedules of teams playing within the same division should be hacked from 18-19 games down to 13-15 games.
Even those big rivalries have been over saturated with the Yankees-Mets, Dodgers-Angels, White Sox-Cubs, A's-Giants playing against one another six times. Heck that's only one less game than those teams play against some opponents in their own league!
On a few other notes of why this idea has lost its spark: 1.) The games are on virtually everywhere all the time, one can simply order MLB Extra Innings and watch any team, any player any time. That is also another reason why the popularity and viewership of the All-Star game has dropped over the last decade or so. 2.) With free agency players switch teams and leagues and cities practically all the time. 3.) For every good rivalry there's always a Houston-Minnesota series.
Maybe it doesn't have to be completely abolished but it would heap a great deal to mix it up a bit.