Why bother with rman? I've stumped everyone with the previous question about how rman would rather consume infinite disk space than remove obsolete backups. That leads me to this question:

datapump backups work (I have actually tested restoring them), and they are easy to manage unlike rman (if you want to dispute this, answer the previous question!) so why shouldn't I just disable the rman backups and consider that the solution?
It is not the fault of RMAN if the person using it does not know how to configure the database.

With RMAN you can:


restore your database to any point in time in the past that your backups cover, not just the actual state where the backup was created
restore large databases significantly faster (have fun with impdp on multi terabyte databases - especially index building and constraint validation, or tens of thousands of partitions, where Data Pump does nothing for hours because it "processes metadata")
backup directly to tape/network/whatever through using 3rd party backup solutions (IBM TSM, Networker, Netbackup, Data Protector, etc.)
have a central inventory of backups, have automatic deletion based on it
compress backups directly without licensing Advanced Compression option (OK, it is not a true  technological advantage)


What you can not do with RMAN effectively/easily (but still possible combined with Data Pump), and where Data Pump shines:


restore a specific object (table, package, etc.) or a subset of objects