1) Less teams means you can get to know your division mates better. Then we can say that division rivalries are a key component of BB. ;-)
2) Every team has a better shot of promoting (instead of 1/16, 1/12).
3) The top 6 make the playoffs, the bottom two relegate and the remaining 4 battle it out for the last 2 demotion spots. You wouldn't have a 5th place team in no-man's land (it is actually better to finish 6th than 5th in the current format - you get revenue and more training)
4) The division will equilibrate faster. The worst teams will demote while the best stay in the division. Right now, with an unbalanced conference, the worst teams often stay up.
Finally, it would force the higher level teams to spend their money and max out their salaries. It makes everything more competitive faster. If you don't spend your money, you'll get left behind.
As for the playoff, that's easy. The top 2 teams get a bye through the 1st round.