The answers here are correct: Control of the pupil magnification during the design of the zoom will maintain a fixed f/# over the entire zoom range. The trade-offs are larger optics or greater number of elements (increase of cost to maintain the f/#). Photographic zooms have a relatively small zoom range (I've designed 20x and 100x infrared zooms), so that particular trade-off isn't a big one in your world...I could see it being taken into consideration within the details of the design requirements (specific focal length range, size/weight, and price point).
I think that I now have a clearer understanding. I had assumed, correctly, that maintenance of a fixed aperture involved a bit of 'waste', in that the front element was, at some focal lengths, bigger than it had to be. Thank you. - David Lyga
It's not always wasted, and it's not a function of maintaining a fixed f/#. I've seen all cases. What actually happens often in a zoom design is that at some zoom settings (typically the shorter focal length), the light rays for different field angles intercept the front element at different distances from center. At other zoom settings (typically the longest focal length), the rays for all field angles come close to filling the front element. It's all in the details of the design. This is most clearly seen in a cutaway ray trace. For example, consider the cutaway layout below of a classic 100-200mm f/5 zoom for 35mm format. This shows optical elements and light ray paths for four different zoom settings ranging from the shortest focal length at top to longest focal length at bottom. The different colors represent different field angles. Blue is 0 degrees and red and green are increasing field angles (the actual numbers aren't important). In this particular case, the maximum f/# is fixed at 5 throughout the zoom range. As you can see, pretty much the entire diameter of the lens elements are used throughout the zoom range. This is advantageous in some cases from a stray light perspective, but it often depends on what can be reasonably traded off.
So bottom line, fixed maximum f/# is fairly easy to design for and is often specified in the design requirements, but sometimes the customer doesn't care or other things are important (like cost and size) and so it isn't. To be honest it doesn't really impact the overall design process for a zoom system or even compared to a fixed focal length lens except for added mechanical complexity.
One other thought: If I needed to reduce the size and weight of this design, I could reduce the diameter of the front two elements by a couple of millimeters. This would trade off vignetting at longer focal lengths for reduced size and weight..