Actually, most people do because they understand that sports photography is a very demanding form of photography, on the shooter and the gear. When people buy a DSLR they are not buying a camera, they are buying into an entire system. Nikon and Canon have the most complete systems on the market today, especially for those more demanding needs.
OP, look at all the systems, they all have their good points and their bad points. But also do some research into what is needed in the way of gear and gear specifications for wildlife and sports.
Sports, unless everything you are shooting is in early afternoon daylight requires fast glass. I don't own a lens slower than f2.8. Night time and indoors you have to have fast glass. Just a nature of the business. For outdoor sports you also need long glass. 70-200 is a minimum lens and is usually a second lens for a sports photographer. My general outdoors lens is either my 30mm f2.8 or 400mm f2.8 depending on the sport and where I will be shooting from. Indoors, again you need fast glass. Often in the way of fast primes.
For wildlife you need reach and at least fairly fast glass. 400mm is generally the minimum focal length you want for wildlife. Urbanized birds and squirrels you can go shorter, but for true wildlife you are going to need reach. Again unless you are shooting in the middle of the day, fast or at least faster glass will be needed.
It doesn't come cheap. High ISO can compensate some, but you are generally shooting at higher ISO when shooting indoors or in lower light. Figure out exactly what you want to shoot and then research the gear specifications for what it is you want to shoot. That will make your decision easier.