Isn't a schemaless database just a filesystem?
I find that MongoDB tends to perform at least as well as an SQL based solution in general use. Some use cases are better suited to SQL (anything with multiple records in a single transaction as a hard requirement for example). It really depends on your needs.
MongoDB specifically allows for additional indexes to be used as part of general queries, or the aggregation methods available. MongoDB even has some nice built in features for querying against geolocation data. They do have some limitations, but in general it works quite well.
Your analogy comparing non-sql to a trashcan is a bad comparison... a better comparison would be to a set of file cabinets.