Headsets are to be used if supplied. But this isn't always the case, especialy during the quieter periods & nights.
I've noticed that the quality of comms in my facility can be different depending on which TX switch I use. The PTT on the headset cable/handset and PTT Pedal transmit fine but the Desk PTT button sends out pure ****e.
Suppose it depends on lots of factors: Headset/Handset quality, Communications equipment, Software issues, and local procedures & practices. Any low quality comms should be reported straight away on the frequency. If it's down to the controller's RT technique (or lack of) it should be sorted without delay. Spare headsets/handsets are always (sometimes) available. And if it's a hardware issue, we have main & standby transmitters and fall back comms.