The entrance pupil is limited by the diameter of the front element, and that is what usually restricts the maximum aperture of telephoto zoom lenses - not the physical size of the aperture diaphragm.

The physical size of the diaphragm is only part of what determines the maximum aperture, expressed as an f-number, of a lens. Magnification between the front of the lens and the location of the diaphragm also plays a part. The f-number of an aperture is determined by the ratio of the lens' focal length divided by the diameter of the entrance pupil, often referred to as the effective aperture. In simple language, the entrance pupil diameter is defined by how wide the opening of the diaphragm appears when viewed through the front of the lens.

When constant aperture zoom lenses are moved to change the focal length, the magnification between the front of the lens and the diaphragm is what normally changes, not the physical size of the diaphragm. The change in magnification is what allows the entrance pupil to appear larger at longer focal lengths and smaller at shorter focal lengths. A 70-200mm f/2.8 lens has an entrance pupil 25mm in diameter at 70mm and f/2.8. At 200mm the entrance pupil at f/2.8 is a tad over 71mm wide. The actual physical diaphragm is the same size in both cases. What has changed is the amount of magnification between the diaphragm assembly and the front of the lens.

Note that this same principle is usually in play with variable aperture zoom lenses as well. Take, for example, an 18-300mm f/3.5-5.6 zoom lens. At 18mm the entrance pupil for f/3.5 is roughly 5.14mm wide. At 300mm the entrance pupil for f/5.6 is over ten times that at 53.6mm wide. Notice that most zoom lenses that max out at 300mm and f/5.6 have front elements that are slightly larger than 54mm in diameter. The needed entrance pupil size is the reason! If the entrance pupil at 300mm were still 5.14mm wide as it is at 18mm and f/3.5, the maximum aperture at 300mm would be f/58!

So why don't all zoom lenses use enough magnification to remain at constant aperture throughout the entire zoom range? Primarily the cost associated with the additional size, weight, and complexity needed to produce a constant aperture lens.

An entrance pupil can not be much larger than the diameter of the lens' front element for a lens with a narrow angle of view. At 200mm an f/5.6 aperture requires an entrance pupil almost 36mm in diameter. Most current interchangeable lenses are at least that large in diameter since the mounting flanges on most contemporary interchangeable lens cameras have diameters roughly 42-54 millimeters. (Please note that we are talking about the width of the hole in the mounting flange, not the distance of the mounting flange in front of the sensor/film plane which is referred to as registration distance.) On the other hand, at 200mm an f/2.8 aperture requires an entrance pupil roughly 71.4mm wide. That requires the lens to be significantly larger in diameter than the hole in the mounting flange.

Not only does the lens barrel and all of the parts of the lens that surround the optical path need to be larger and thus require higher quantities of the raw material from which they are made, but the actual optical elements must also be both larger in diameter and thicker in order to maintain the same refractive angles. The larger lens elements also introduce more aberrations that need correction. Often the most expensive materials in a lens are those used to make these corrective optical elements. Adding elements to correct things such as chromatic aberration can introduce additional problems, such as geometric distortion, than require even more additional elements to correct. So not only does the entire lens and many of the optical elements inside need to be larger, but it also requires more optical components made from more expensive materials. This means not only is the lens more expensive to design and manufacture, but it is also larger and heavier.

For most folks, unless they really need that larger aperture they would just as soon carry around a lighter, smaller lens for which they paid a lot less.