I think an important advantage is saving time. When you happen to shoot hundreds of photos in a row stuck with a lens wider than would be optimal, cropping each one of the images into a smaller size in post processing would be quite tedious - usually you can't do that in batch unless you really don't care about resulting framing. Framing on spot, on the other hand, is something you'll have to do anyway.
When you're shooting less-than-maximum resolution JPEGs, digital zoom will retain more image information than you'd get by cropping later. E.g. when shooting 6MP images with a 16MP sensor, cropping a half-height-half-width image will result in 1.5 MP of information, whereas using digital zoom on spot would store image based on information of 4MP.
In some cameras (such as my old Panasonic DMC-FZ30) digital zoom is equal to extra optical (tele) zoom when you are shooting video or photos with less than maximum sensor resolution (e.g. for web use only). Using digital zoom, the camera would use smaller area of sensor to compose the picture, but not less pixels than in resulting file.
I mostly shot water sports for web / computer display with that camera and found the extra reach with 3MP much more useful than full 8MP resolution. With the extra zoom, the person was larger in EVF for lining up with a focusing point (quite hard with extreme zoom and subject speed), the files were smaller, and I had to spend much less time at computer. For example, this picture would've been hard to focus using full resolution: