Can I change my host header for my webapplication simply by adding a new binding in IIS, and changing the AAM for the default zone to the new URL?
You have to do more work as Russ mentioned in his blog. he very well explained the reason, "making any change to Web Application settings without proper way, will not update the configuration database". So when we have an issue with SharePoint farm, sharepoint will knew old host header url.
Extending and un-extending the web application is way to go with it, it is little pain in start but more reliable. when you do this, make sure do it in off hours, it will cause the outage.