I looked into doing an African safari a couple of years back, but for the places I really wanted to visit I was surprised at just how damn expensive they are. It's not uncommon to be spending over $1,000 per night at some of the established camps in places like the Okavango.
Not sure what places you are referring to but I did a self-driven safari early this year in Kruger (South Africa) and even though it was definitely an expensive experience compared to the rest of my trip, it was well below that amount. These are approximate amounts, but I think that including the car rental, the daily entrance fee to the park and staying overnight, all together was around 50-60euros per day. Guided tours that span over multiple days tend to get quite expensive, I agree. And there's plenty of high-end accommodation and travel packages. But there are also ways to experiencing it without spending a fortune.