Is there a good reason to have a handheld Aviation Microphone in GA?
According to the 172 Minimum Equipment List from Cessna (S and R models)



these are both Category C items which the MEL states 


  Category C: Items in this category shall be rectified within ten (10) calendar
  days, excluding the day of discovery.


So it looks like you may need to fix it but in the event you are flying it looks like you need an alternative (headset should do that) and or a backup headset on hand. 

However the 4th column states that zero are required for dispatch so you can fly without it. 

As people are noting in the comments in a lot of planes these mic's go more or less unused or are inop these days. I know I have never personally used one in any of the archers I have flown.