O, my... I went this direction, made my reasearch, and I will rephrase the question.
There are no "other African countries" where you can happilly go hunting, on budget.
There is only South Africa and Namibia. (Speical cases) Full stop.
The reason for economic pricing there is system of succesful game ranching, or game farming.
You can hunt on a budget on the farm, And in many cases in low or high fence. And in some cases (Namibia, farmland, and conservancies) out of fence, limited number of species.
A lot has been written here on the forum about fenced hunting, but do not jump to conclusion, it is not free range, or that every farm is "put and take - ear tagged animals". Certainly it is not the case
The farms are triving, full logisitc is set up and in place, transport established (mostly by roads, with some cases by charter plane) and then you also have healthy competition where pricing is acceptable, on supply and demand basis. Foreign hunters are coming in large numbers.
It is my estimate 80% of all safaris are conducted in South Africa and Namibia. And maybe 20% of safaris in the rest of Africa. Game farming, gave us the otpion, first time in history that middle and working class western hunter, can finance, go to safari and taste Africa.
South Africa and Namibia are also, a great conservation success, as the numbers of game continously grow. These two countries saved from extintion number of notable species by this system, on hunters dollars, to name few: rhino, black and white, black wildebeest, bontebok, etc....
You move away to safari in African true wilderness - away from farm land - say in Namibia, you will get similar prices as "the rest of" Africa. (Check for example pricing for safaris in Caprivi strip, Namibia)
But this is not then "a farm", it is wilderness. Concession fees, camp staff, anti poaching team, flying by local charter plane, maintenance and logistics of camp in wilderness... etc...
I was reading recently an old article, in Gun Digest, issue of mid 50-ties. Lets say 1955 (approximately), good full bag safari at that time, hunting 1-1, the price estimated then was 10.000 USD (Tanzania, Kenya, Uganda - All east Africa). This safari will include some of big 5, but not all.
Historically converting money from 1955 to today, would be cca 100.000 USD. (infaltion calculator available online). Pricing does not change too much, after 7 decades.