In some cases, a $sort aggregation stage can swap with a preceding $project. Consider the following example:
An explain of this aggregation shows that a COLLSCAN will feed the $project => $sort pipeline. If the agg optimization phase were to swap the $sort with the $project, however, it could push down the $sort and obtain the desired ordering via an index scan. This would remove the sort stage from the query plan entirely, which could result in a substantial performance improvement.
We would probably want to apply this optimization only if the query planner's sort analysis shows that the sort can be obtained via an appropriate index scan.