In Sanger sequencing, why do we resort to cloning? Why doesn't PCR suffice?
The error rate of PCR is still very high in comparison to natural bacteria DNA replication of its plasmids. 

Natural bacteria DNA replication has an error rate of approximately 1 in 10 billion, and the best PCR polymerase commercially available (Q5 from NEB) has an error rate of approximately 1 in 1 million. 

Therefore, cloning fragments into bacteria and sequencing the cloned plasmids ensures that you have the correct sequence for further downstream experiments, since the error rate of natural plasmid replication is far lower. With PCR, you are likely to have some errors introduced due to the higher error rates. This becomes more and more likely with increasing numbers of PCR cycles as well as increasing PCR amplicon lengths. 

The fact that the PCR amplicon sequences correctly does not mean that DNA cloned from the PCR amplicon is correct. Therefore, if the PCR is intended for downstream experiments, it is best to sequence the cloned plasmid instead of the amplicon. 

In addition, as WYSIWYG has pointed out in the comment, having the PCR amplicon cloned into a plasmid would also allow for the plasmid's regions flanking the cloning site to be used for sequencing. This allows standard sequencing primers on the plasmid to be used, instead of having to design new sequencing primers for each PCR amplicon. 

Furthermore, since Sanger sequencing requires the primers to bind ~50-100bp upstream of the region to be sequenced, cloning the amplicon into a plasmid would also allow short amplicons to be sequenced in a single read, instead of requiring a forward and reverse read for sequencing a PCR amplicon.