It doesn't. The haptic motors which provide vibration and tactile feedback can be used to produce sound.

Remember those floppy, printer, other old hardware noise music videos? Something like this one. Steam Controller works kind of in a similar way. Tiny motors are able to squeak fast enough to produce multiple waveforms that mimick sound.

Plenty of controllers do. They can be used for multiplayer in place of a headset. Some games will also use them for non-world audio, like an audio log or a mission update. You can also use them in conjunction with haptics for communicating menu interaction. A different timbre of click for allowed vs disallowed, for example.

The playstation controllers have a speaker. A lot of games use them for interesting things. Like in some games where you can find voice recorders, the recording will play through the controller as if your holding it.

Read in a game review that used a PS (?) controller speaker for radio messages that this worked great for immersion