From what you have said so far it seems you want a even more liberal policy, where these countries would be flooded with immigrants in maybe one decade, until they broke down
What makes you think everyone would move if they could? Most people like to stay home, unless home is not a good place to live.
Population explosions in Africa are projected to lead to much more people wanting to move than now actually. In general, Africa is not a good place to live compared to the west
