I remember when the Milwaukee Brewers were in the American League West and were called the Seattle Pilots (1969).
The reason there is the odd configuration of divisions is because if they divided the 30 teams into two 15 team leagues with 5 teams in each division there would have to be at least one inter-league meeting every day. That's hardly a way to market the concept each year as something "special" as they currently do every May/June when it's inter-league season.
Or they could just give one team in each league a day off. Not every team has to play every day, and they currently don't anyway. It might make the scheduling a little difficult to manage, but it's not at all impossible. Leave it in the hands of MLB and they'll probably screw it up anyway though.