Air conditioning requires a power source to run. The parts of Africa I know do not have a steady supply of electricity, and even if they did, it is an expensive luxury for most (you do not need it to survive).
Even in Hawaii, where the climate is similar to parts of Africa (there are so many micro climates across Africa it is hard to say exactly which you mean…), air conditioning is often considered a luxury. It is prevalent in the city but uncommon in rural areas. City folk are such pansies. They are afraid of sweat and fresh air. They also insist on formal dress (long sleeve shirts, slacks, fully covered dress shoes, sometimes suits) so that they require AC to stay comfortable. People should be more reasonable. In climates like Hawaii, people should dress accordingly. Then you wouldn’t look stupid walking around outside, and you wouldn’t need to cool buildings down so much.
I grudgingly designed air conditioning for a living for a while (grudgingly because I also view it as an unnecessary luxury in tropical climates where temperature varies maybe 10 degrees over the year and no one is going to die of heat stroke or frost bite). Expensive is a relative term so I’ll say that it is a hefty added cost. In commercial buildings, energy cost due to HVAC can be 30% of the total cost of electricity or more.
Indoor air quality in an AC environment cannot compare to fresh air. Industry would debate this, and point to their standards for fresh air, but the fact is while AC may not be terrible for you, fresh air is always better. You can design an AC system to supply 100% outside air, but this is not viewed as economical because you have to treat all of your air constantly which requires energy (as opposed to recirculating most of it and treating just a little bit of fresh OA).
In tropical climates with tradewinds like Hawaii, there are a lot of passive methods for achieving adequate ventilation and comfortable temperatures. Large overhangs, openable windows, orienting large glass windows towards the north or south as opposed to east or west (particularly west as afternoon sun is the strongest here), creating a bit of stack effect, good insulation, presence of water or shady areas in the wind path of your house to cool the air before it enters are some of the ways you can stay comfortable without needing AC.
I think good city planning also helps. It has been proven that cities are heat sinks in themselves.