This sounds great, but in practice is impossible. Are you personally as an individual going to take care of 100% of your own backups? Are you going to drive the tape over to the other facility that you own, make regular checks that you can restore, etc? No.
Ultimately you are going to rely on someone else and something else. Be it your IT guy, the company that hosts your backups, the power company, the company that makes the machines you keep your backups on, etc. You can distribute this so that you rely on lots of someone else's and any one or more of them can fail, but often you'll still have one point of failure somewhere (the guy who monitors the distributed backups for example).
I mean each organization needs to have in-organization backups and each individual needs to back-up their machine.
Yes, my IT guy. I need to have an institutional relation with my backup guy, not just a paying relation. The IT guy could send the data to three different online backup services but me having a personal and institutional relation with him makes sure that whatever scheme he uses will remain reliable as other things change.
The point is that every organization has at least one mission, one task that it is worth doing within the organization rather than offloading to another entity. And backup is always going to be close to that mission.
Ultimately you are going to rely on someone else and something else. Be it your IT guy, the company that hosts your backups, the power company, the company that makes the machines you keep your backups on, etc. You can distribute this so that you rely on lots of someone else's and any one or more of them can fail, but often you'll still have one point of failure somewhere (the guy who monitors the distributed backups for example).