The performance of the suggested answer is fine. According to the MongoDB documentation:
When a $sort immediately precedes a $limit, the optimizer can coalesce the $limit into the $sort. This allows the sort operation to only maintain the top n results as it progresses, where n is the specified limit, and MongoDB only needs to store n items in memory.
Changed in version 4.0.
So in the case of
db.collection.find().sort({age:-1}).limit(1)
we get only the highest element WITHOUT sorting the collection because of the mentioned optimization.