What are use cases for *not* resetting a groupby index in pandas
When you perform a groupby/agg operation, it is natural to think of the result as a mapping from the groupby keys to the aggregated scalar values. If we were using plain Python, a dict would be the natural data structure to hold such a mapping from keys to values. Since we are using Pandas, a Series is the natural data structure. Its index would hold the keys, and the Series values would be the aggregrated scalars. If there is more than one aggregated value for each key, then the natural data structure to use would be a DataFrame. 
The advantage of holding the keys in an index rather than a column is that looking up values based on index labels is an O(1) operation, whereas looking up values based on a value in a column is an O(n) operation. 
Since the result of a groupby/agg operation fits naturally into a Series or DataFrame with groupby keys as the index, and since indexes have this special fast lookup property, it is better to return the result in this form by default.
When working with groupby on a pandas DataFrame instance, I have never not used either as_index=False or reset_index(). I cannot actually think of any reason why I wouldn't do so. Because my behavior is not the pandas default (indeed, because the groupby index exists at all), I suspect that there is some functionality of pandas that I am not taking advantage of.
Can anyone describe cases where it would be advantageous to not reset the index?