There's surprisingly much more depth to the system than it first appears. There are multiple mechanics with regards to the Brave/Default system which aren't obvious until the game really gets going. Default on its own has many, many advantages - it's basically the "block" command, it stores up an extra action you can use later without penalty, and it prevents you from going into the red.
How much BP you and the enemies have also determines if you could possibly have a full other turn before the enemy can act again, or vice versa. Ending a turn with negative BP while the other side has positive or 0 BP will mean an entire turn where that character is vulnerable to attacks without being able to block at all.
There are also skills which use BP instead of MP, and skills/abilities which play around with BP in interesting ways, like providing bonus BP when certain conditions are met, or using BP as a means of determining bonuses.