I have a Cessna 172P in which the handheld microphone has stopped working. Before I replace, I was wondering if there is any good reason to even have one? I have PTTs on both the pilot and copilot, yoke.
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.
Ask yourself the question; you call tower to respond to an instruction or something, and there is no response, or tower starts calling you because they haven't heard from you even though you thought you'd talked to them, and you need some kind of standby device right now to talk with without having to fumble around. Be nice to be able to grab a mic that normally just sits there unused.
Maybe you have a spare headset on board, but imagine having to fumble around to get it out and plug it in while your attention is needed elsewhere.
So if you have a spare headset plugged in and ready to go that you can grab without much effort and use, not a big deal, but if that's not the case and you fly in controlled airspace a lot, I would say you should have one.