Lot of assumptions in the question that need unpacking.

A couple of baseline points. First, Africa (including North Africa) is huge. You may have seen map projections that more accurately communicate its relative size compared to a Mercator projection.

Second, you're understating linguistic diversity in many other regions besides Africa, in part because many contemporary nation-states have an active interest in understating or undermeasuring that diversity. Take Spain: you could maybe just say that Spain has Spanish and it has Basque. Speakers of Catalan, Galician, Aranese and Aragonian might differ with that representation, particularly speakers of Catalan. In much of Western Europe, communities whose languages are related to but still different to the dominant official language were strongly suppressed in the 19th Century but not wiped out. They're still there, and in some cases in roughly equal percentages to some minority languages in sub-Saharan African nation-states. This is equally true for much of the Middle East, Central Asia, South Asia, South-East Asia and East Asia. So your perception of a strong divergence is overdrawn.

Third, in areas of especially dense linguistic diversity in sub-Saharan Africa, many people are at least bilingual, sometimes far more so. Sometimes neighboring languages are relatively closely related, sometimes not. There are widely distributed majority languages and very infrequently spoken minority languages. If there's a difference overall, I think you could say that postcolonial African nations were sometimes combinations of regions and peoples who did not have strong pre-existing interactions and that those states were sufficiently weak in a variety of ways that they did not undertake the same oppressive projects that 19th Century European (and some Asian) nationalists did to suppress minority languages. Or if postcolonial nation-states attempted to suppress one language or dialect, they often failed to do so (or inspired secession movements because they tried).