It's actually an interesting point that whilst wide aperture lenses are popular for wildlife photography, f8 is actually used a lot more than people think. Mostly because depth of field at long focal lengths and great distances requires a smaller aperture to actually get the majority of an animal in focus. Of course wide aperture lenses come with the option of shooting wider in lower light and also the added light improves AF performance.
The 600mm mirror lenses are generally frowned upon because they can create doughnut shaped rings in the background highlights which are often considered undesirable. They also tend to be somewhat slower to shoot with in terms of focusing and light gathering. Their main bonus is, however, that they are very compact and light compared to regular telephoto lenses of similar focal lengths.