It seems you misunderstand what the sysdba privilege is and how it is managed:
The SYSDBA privilege is needed to perform some operations (create/drop/alter database, start or stop an instance, ...).
When you connect to a database using this privilege, it is as if you were connected as user "sys".
Due to the fact that the SYSDBA privilege is needed to startup the instance, the control of this privilege is manage outside the database, ie in a group at the OS level.
This group is named "dba" on unix server or "ora_dba" on windows boxes.
All the OS user accounts that are in this group are allowed to connect to the database with the sysdba privilege, even if they don't have an account inside the database.
And as said in the documentation RMAN must be run with the sysdba privilege.
Indeed, this user is allowed to drop any objects in the database without restriction but this is because RMAN should be run only by a dba not by some random users.
If you want to allow a user to export some objects you will have to do otherwise. If you use oracle 10g or newer, have a look at datapump.
With datapump, a DBA can choose a folder on the server, where some users could export some objects.