This is true, and good to know but with caveats. If you take the picture in 16:9 mode then yes you're only using part of the sensor (or likely the whole sensor but only part of the image is being processed and stored), but you would also be using your phone's display to properly frame and take the picture how you want to. A good picture is not just the technical aspect of using the sensor.
The outcome when someone crops a 4:3 image after taking it to make it 16:9 etc depends on how the orignal image was framed and how good the skills are of the person cropping it. You may get more information if you take the picture in 4:3 mode but then you may find it much harder to convert it to a format you like (for example, a format that would fill the display when viewed on a phone, a TV or a computer display) due to how you framed the original photo. I'd argue it's better to take the photo in the format you want to consume it in if you're using a phone. If you have an actual dedicated camera, then get a camera that works best in the format you want to use.