However, many hosting providers just do not provide the solution that you suggest. And in any event, you are now subject to a localised outage that includes you and your host.

The solution is a to use a third party service like edgedirector.com which offers a failover feature. With their service you can even failover to a second failover that they maintain for you. That is exactly what one media company did. They created their main failover site to backup production, and then if even that becomes unavailable, they failover to the third level of redundancy provided by the vendor.

As a specialty service, they can provide a level of service and flexibility that your host may not be interested in providing.