Just because you tick a checkbox doesn't mean it'll actually work as planned, and unlike infrastructure within your control that you can actually test (pull the network or power cable from a live server if you need to), you can't simulate a cloud provider outage.

> multi-AZ or even multi-region is much more straightforward than renting another rack somewhere.

Assuming that enough of the AWS control plane is alive to actually allow you to login and administer the services in your backup region.

Furthermore, cloud providers are their own businesses and are constantly in motion (introducing new features, etc). That's good for their business but bad for yours, as it means they might be doing risky changes that could affect you should it go wrong.