The Microsoft Xbox App doesn't even provide an option to enable Push-To-Talk on the PC which is a fundamental failure and the reason I don't ever join Xbox Chats.
I'm playing on a Gaming Notebook which doesn't have a mute button for the mic and generally like to not use a headset and also like to set up different Push-To-Talk Shortcuts for TeamSpeak, InGame Voice Chat, Discord, ... to easily control who I'm talking to.
There is a free solution for the PC users though: MicMute (it mutes/enables or adjusts the volume of the mic globally via keyboard shortcuts, overriding the Xbox App)
MicMute (Google Code Archive)
MicMute (SourceForge)
This does override all other software like TeamSpeak, Discord, Mumble, ... as well though.
There's constantly kids on with parents or brothers around screaming and shouting, people coughing or talking to somebody else in their room, hearing any noises in their room and that is irritating and prevents me from understanding what others are saying or who is talking even.
Even though I don't join any Xbox Chats plently of players on the Xbox don't have any PTT in place and cause the above mentioned through the ingame chat.
Sometimes I'm listening to music while playing, or am talking on the phone or to anybody in my room and don't want others to hear it, especially when it is important or private.