According to David DuChemin, you can't zoom with your feet. At least that's what he asserts in his post today on his blog.
Of course, he's absolutely right. Zooming - changing focal lengths, that is - with all the attendant shifts in field of view, depth of field, compression and whatnot is inherently different than simply getting closer or further away from your subject.
Here's a simple real-world example that I concocted with stuff lying around in what passes for my office. Apologies for the overall crumminess, but these images are useful if anything to make a point.
Notice the can. In both images, I deliberately framed the shot so the can would be nominally the same size in the frame. That is, the can takes up 1/3 of the frame (vertically) in each image. These images were shot using the same camera (Fujifilm X-T1), the same lens (18-55mm f/2.8-4.0) and at the same height (using a monopod). Nothing else changed: the subjects were not moved, the shutter speed, flash power, exposure compensation etc. The only changes were the position of the camera along the Z-axis (front-to-back) and the zoom setting on the lens.
Now notice the foreground and background elements.
In the image on the left (Fig. 1), the bottle appears relatively small and "far" away. The edges of the chintzy backdrop board are visible on either side of the frame. The front of the cabinet is darker - the camera was so close that light from the flash didn't bounce the same way as in figure 2.
In figure 2, everything on the Z-axis is compressed; the can appears to be closer to the edge of the cabinet, and the bottle closer to the can. The bottle looms large over the can, too. It's slightly blurrier as well, due to shallow depth of field.
So what does this mean?
Well, yes you can use your feet to make your intended subject the size you want it to be in the frame. But what's going to change is everything else - the elements you'll wind up inadvertently including (or excluding) from the frame.
But this isn't zooming, of course. It's reframing.
What's appropriate all depends on your vision and your constraints. Do you want to carry around a light, pocketable camera, or a backpack full of gear? What are you willing to give up? There's no objectively right answer.
Some people claim to become more creative and produce better images when they have constraints such as a single focal length. Either you can get close enough to your subject or you can't. Same goes for landscape or architecture photographers, who might or might not be able to get far enough. So you look for a different angle, point of view or element to focus on.
Personally, I embrace using a compact, single focal length camera. But this isn't out of some sort of artistic purity or self-flagellation or some smug, obnoxious bullshit reason that the holier-than-thou prime lens purists espouse. This is about being out all day with a single, small camera that I can barely feel hanging around my neck. When I wear a camera with a zoom lens, it's always bulkier and clumsier and doesn't feel "right." But that's just me. Not to mention, the zoom is never "fast" enough, so I feel compelled to pack at least a single fast prime for nighttime etc. That stuff adds up real quick in a backpack.
I've traveled light, with only a Fujifilm X100S (a single-focal-length compact that forced me to "zoom" with my feet) and I've traveled with a full kit (the aforementioned X100S plus a Fujifilm X-T1 and 3 lenses). After having looked over my images from both trips, I can say with certainty that I had a much higher "hit rate" using only the X100S and living within its constraints. Not futzing around with lenses is liberating. My back and shoulders were also thankful at the end of each day. Plus, my family got somewhat less annoyed with me.
Until the laws of physics change and I can get a pocketable camera with an APS-C (or bigger) sensor and an 18-55 (or longer) fast lens in something the size of Fuji's X100 series, I'll stick to reframing with my feet.
But I won't zoom.