Considering we are talking about countries which are smaller than some US states, consider how you, as a citizen of your state would feel if some foreign government bombed your state for two months. Every day you wake up and wonder which city in your state will be bombed today.
By adopting a strict policy of requiring Congress permission for every military campaign (even a single drone strike) would allow notions of peace and diplomacy to win over notions of war. Consider this - if a military action is truly required, Congress may hold an emergency session whatever time or day it is. If it gets pulled into a debate, then the target has time to agree to a diplomatic solution, and diplomats have a chance to resolve the issue without further bloodshed.