I always saw a DBA as someone who fits in between developers and operations when it comes to database management.
On the one hand, they often take care of backups, clustering, replication, actual binary installation, file system management, etc.
On the other, they also take care of relational DB schema, do performance or query optimization, and advise developers on the best way to lay out their application storage and configuration schemas.
In theory, the first job can be done by a system administrator. The second job can be done by a senior developer or architect.
In practice, it often makes sense to have someone who's well versed in all parts of running a database.
Provisioning the instance is only a small part of what they do. Having your instance hosted in the cloud doesn't remove the need to have someone manage your schema or optimize performance. A cloud RDS with default settings likely won't be aware that key_buffer_size value needs to be set to 16M or some of your application's features won't run.