This is the only way in which you can enjoy the social parts of the game, such as sending/receiving gifts, posting winnings, adding friends, etc.
Moreover, in case you are playing Bingo Blitz application from a mobile device this is the only way in which you can save your in-game progress if you encounter situations like phone stolen, reset factory settings, switching phones, etc.
Please be aware that your account information is only saved when you are connected to Facebook, therefore should you ever have issues or replace your mobile device, you will not be able to retrieve your previous progress, unless you are connected to Facebook.