One use case for different labels is process modelling. Sub-processes are often modelled using groups. In expanded state, the grouped entities "describe" the sub-process and hence a group label is unnecessary and thus omitted. In collapsed state, however, the grouped entities are not visible and a descriptive group label is very much desired.
The label sync is not enabled by default because the default behavior for label text is consistent with the behavior of all other group properties. (Color, size, etc. may be different for collapsed and expanded state as well.)