I also use the ENV approach.
The key advantage is resilience / agility - as long as I have the app.yml, I can relaunch my site on a new server with minimal fuss. Or manipulate a staging server with ease.
Also, this tends to be something that you sort out once, when you establish a site. Or maybe perform as a one-off upgrade. So it suits ENV nicely.
Having said that, it is also helpful to have the settings available for troubleshooting without the need to rebuild; once the settings are stable, they can then be migrated to ENV settings.