Is there a reason to use 4 diodes instead of 2 when controlling a motor with L293B?
What would be wrong with just connecting Output 1 and Output 2 alone
  to the motor?


In your 2 diode diagram you have the motor completely shorted out: -



4 diodes are needed when you have a full bridge driver to ensure motor back emfs  adequately push excess motor energy (due to inductance) back to the supply rails. You also need a reasonably good reservoir capacitor on those supply rails too.