A small opportunity for optimization on queries using sparse indexes:

assert.commandWorked(db.c.insert({a: 1}));
db.c.createIndex({a:1}, {sparse: true});
db.c.explain().find({a: {$exists: true, $eq: null}});

The bounds we get are:

{"a": ["[MinKey, MaxKey]"]}

Since the query only searches for literal null, I believe we could use tighter bounds which only include null and undefined (something like [[null, null], [undefined, undefined]]