@Kyoko To add to this, here’s a decent article on the notion that the invention of the wheel wasn’t as easy as everyone tries to make out: https://www.scientificamerican.com/article/why-it-took-so-long-to-inv/
It was probably not ‘invented’ by multiple societies, but rather spread itself around into different civilisations. You then have to ask why areas such as North West and Eastern Africa didn’t adopt the wheel despite having long-established cross-cultural and trade links with the Middle East and, by extension, Europe. (They knew about the wheel and had the technological level to create it in these northern, western and eastern African societies. This is asking why it wasn’t adopted on a large-scale like in Europe, etc.)
The answer is probably that it didn’t really, in their eyes, improve efficiency that much. As has been well-established by multiple studies, much of Africa’s soil is pretty light, which reduces the need for ploughing. They also lacked a lot of large animals to tame to carry things over long-distances, bar camels. Top that up with a large abundance of slaves (European slavers surely would have traded anything for slaves when active there in the 1500s, further hinting that there wasn’t much of a demand) among other things and you see why the wheel never really ‘took off’ as a means of improving labour efficiency in Africa. I’m certain it existed in some parts at the same time, but it wasn’t widespread.
Also, it’s worth saying that a lot of West African societies rivaled European societies around 1400-to-1600 AD. They had comparable levels of wealth, and had armies of similar levels. I’m pretty sure they repelled a couple of European invasions too.