I probably bring history and literature into responses too often, but they tend to be useful in explaining things. We can thank the British East African safari experience of the decades before and shortly after WWII for the typical tented safari experience one finds in South Africa and some areas of Namibia. Whether carried by a battalion of porters, are more typically a 2 1/2 ton lorry, the East African Safari Camp was as comfortable as could be created in a wilderness environment - the sort of standards listed in
@Kevin Peacocke ’s post. That type of safari experience was portrayed to one degree or another in every book and movie about hunting Africa for the better part of four generations. When hunters dreamed of Africa, those camps were part of those dreams.
If we flash forward a hundred years to modern South Africa, many outfitters offer a modern replica of that traditional environment. This is a contrived setting in which most clients willingly and happily set aside reality and participate, Rather than a canvas tub and river water, one has ensuite bathroom with hot and cold running water and flush toilets. Rather than a meal served under a canvas awning by lantern or candle light, it is typically in a central open thatched pavilion with electric lighting and likely a bar. And let's not forget the absolute necessity of wifi. It is a little bit of make believe to capture the spirit of safari and the early twentieth century.
To the OP considering bringing his back back tent into such an environment, that would be no more “real” than the permanent tented camp. You would be sleeping in the “bush” in locations easily reached by vehicle from the main lodge or camp on a day hunt. To my mind this is another replication of a wilderness experience - this time a North American one. A parallel would be to book a hunt on Jeff Rand’s 777 in Texas and ask to pitch a pup tent in a back pasture.
To be fair, outfitters have offered backpack hunts into some areas of Namibia for mountain zebra and oryx. Someone may be doing that now. However, I would think of this as a fairly specialized hunt for specific species or two.
The next choice are the semi-permanent camps in places like the Caprivi, much of Zim, parts of Zambia and Mozambique, and the areas of West Africa where bongo and LDE roam. All will be off the electric grid and many will be established only annually due to flooding, rains, whatever. These camps are typically found in dangerous game country so one can often fall asleep to the sounds of hippo or a moaning lion. Temporary tents, often over a permanent slab or huts are typical accommodations. The shower will be a separate shielded area and there will be little doubt that you are not on a game ranch. These settings and hunting environments can often give the client real glimpses of hunting with Hemingway in the thirties or Ruark in the fifties.
For instance, this photo of our crew packing a couple of buffalo several miles out of the Zambezi Delta swamp could have been taken before 1954 as easily as 2014.
And bring a satphone.
Last are what I would term the semi-temporary camps found in the hunting concessions of Tanzania on multi-week safaris. A full bag hunt will require movement to multiple locations where the party typically will fall in on a partial camp infrastructure, bringing the rest from the last location. These hunts are the closest to those experienced by clients in the first half of the last century.
Generally, as the content of wilderness reality increases, so do costs. Unlike the South African lodge or permanent tented camp portrayal which represent initial sunk costs, the typical off grid concession owner, is absorbing substantial annual costs to replicate his offering each year. Because many of these concessions carry dangerous game, they tend to represent a premium investment in lease costs as well. Food, power, access - essentially everything is more difficult to obtain and provide. All add to overhead costs.
I think South Africa is a great place to go for a first safari. The comfortable tent "camp" environment or lodge is perfect for a first exposure or for non-hunting spouses and families. One can fill a trophy room or den on a first trip. Many sponsors here can offer exactly that experience.
However, I expect that you will find like many of us have, as Africa works its way deep into our souls, shopping for a satphone is just around the corner.