everyone else's "natural rival" made sense, and this is what was left. a relic from when "Interleague Play" was a limited engagement, with all rivalry series taking place at around the same time. (they couldn't do the "split rival" thing for this one like [TOR or BOS] vs [ATL or PHI])
It was really fun when our rival changed from year to year and we had to switch off between hating the Padres and Rockies!
i can't relate to the split rivalry thing as a Mets fan - i know the introduction of the Nationals gummed things up, as did Houston's move to the AL (and subsequent onset of daily interleague play). i do like 4-6 Yankees games per year but otherwise don't like interleague at all.
Definitely with you there, and dreading whatever realignment is gonna make it all so much worse!
if they keep the two-city markets separate and maintain the general feel of the AL and NL, there's a chance they could improve things. (the current "play all 30 teams" schedule is possibly the worst schedule rubric in baseball history)... but it could also get much worse!