Small car might be possible
It is possible to travel extensively through East Africa only on tarmac. On a traditional east coast route (ie Cairo to CapeTown) there are only two sections that may cause problems for a small 2WD:
1. Northern Kenya - Isiolo to Moyale is a dirt track. It can vary from very stony rocks and deep corrugations to red dust. It can be muddy in the rainy season - particularly the stretch between Turbi and Moyale. In the right conditions it would be possible to do this in a small 2WD, however the car would take a heavy battering.
2. Sudan - Dongala to Wadi Halfa - some sandy sections, although mostly corrugated track through the desert. There are no dunes, so it would be possible with a small 2WD, although again the corrugations would be the biggest problem.
I think the principal advantage of a 4WD on this route is it allows you to get slightly off the beaten track, whilst being able to carry plenty of camping gear - both of which would be limited in a small car.