As stated in the docs (https://docs.mongodb.com/manual/reference/operator/aggregation/sample/#behavior), the $sample stage will perform a full COLLSCAN if some criteria won't be met. The problem is that no view (https://docs.mongodb.com/manual/core/views/) will ever meet these, as the $sample won't be the first aggregation stage.

My proposal is to implement additional, $skip+$limit based sampling.