The $queryStats execution stage materializes every field in the query stats entry. The stage could internalize a $project and just skip over fields that the project field will remove. This could be modeled like $_internalUnpackBucket which uses an include/exclude field to internalize the projection.

This is related to the $queryStats top-k sort optimization (SERVER-129387), which works with a $queryStats followed by a $project, but should be considered a separate optimization.