Here's an interesting piece from FanGraphs, where they did a better job than we did on the math of the possible new realignment.
Your money quote:
Over the past 15 years this new system would have made the AL almost twice as competitive and the NL about a third less competitive. Overall an extra 0.3 teams would be in a competitive race per year. So the realignment would have slightly, but not drastically, increased number of teams in playoff hunt. Although it would change which teams were in the hunt; the new system would make it easier for teams from good division, e.g. the AL East, to make the playoffs.