The economics are certainly moving, but I think it will be a long time before on-site storage is obsolete.

A reliable fast connection is still very expensive, and there are several other considerations. When we looked at offsite backup a major consideration was restore times. Even if you can do differential backups, in a disaster you might need to get everything back ASAP and even the best internet connection can't get near the throughput of onsite disks/tapes.