A valid question on how much the change in aperture affects depth-of-field, is whether an 70-200mm f/4 zoom would give you the same kind of look that an f/2.8 zoom would.
For me, a fast f/2.8 aperture is essential on a zoom lens, especially the telephoto zooms. For the same scenario, it gives me a higher shutter speed than the f/4 zoom. Or I can use a lower ISO. More importantly, since I often bounce flash in large areas, the f/2.8 aperture gives me more chance of successfully bouncing my flash than an f/4 aperture would.