The 3/5 rule was adopted for apportionment of House seats. Southern colonies wanted to include slave population in the census, but deny slaves voting rights. Northern colonies said they cannot have it both ways - earn more House seats due to slave population, while denying that same population voting or any other rights of non-whites.
Without this compromise, there may not have been a Constitution.
Yes, the southern states pretty much got what they wanted regarding slaves, representation, treaties, and a ban on export taxes.