Is there a way to disable all notifications on the iPhone in one step?
Do Not Disturb does also hide notifications and you can customize it like allow incoming calls from favorites or everyone. 

When the device is locked, it won't light up the screen when receiving a message. But by enabling 'Always' on the bottom of the Do Not Disturb setting page, it will also block the notifications when your device is unlocked. 

So they won't pop up on your screen, you can only see them by opening the notification center.