Storage-as-a-Service is relatively new. Today the main value proposition is as a cloud target for on-premise deployments of backup and archiving software. If you have a need to retain data for extended periods of time (1 year plus in most cases) tape is still the more cost effective option given it's low capital acquisition cost and removability. If you have long term data retention needs and you want to eliminate tape, that's where a cloud storage target comes in. Electronically vault that data to a storage-as-service provider who can store that data at cents per GB. You just can't beat the economies of scale these providers are able to achieve.
If you're a small business and you don't have the staff to implement and manage a backup solution or if you're an enterprise and you're looking for a PC backup or a remote office backup solution, I think it's worthwhile to compare the three year total cost of ownership of an on-premise solution versus backup-as-a-service.