if we are using $expr, we don’t produce covered projections.

If index on a is present,

This will have fetch + projection simple
db.test.explain().aggregate([{$match: {$expr: {$eq: ["$a", 1]}}}, {$project: {_id: 0, a: 1}}])

But this will have projection covered:
db.test.explain().aggregate([\{$match: {a: 1}}, \{$project: {_id: 0, a: 1}}])

It looks like a problem with dependency analysis of $expr that can’t determine that we only need field “a” that can come from the index.

In some cases we have to use $expr syntax. For example, in $lookup with pipelines.