I don't know when I've started having this, but with my MacBook Air 2015 13", the volume icon only shows "Headphones" as an output device option.
The icon is not greyed out, nor is there any red light coming from the headphone jack. The startup chime works fine as well.
- Resetting NVRAM - didn't work
- Resetting SCM - didn't work
- Re-plugging in the headphones (multiple times) - didn't work
- Twirling the headphone plug (multiple times) - didn't work
- Blowing in the headphone jack (multiple times) - didn't work