I'm on Android, Samsung S7.
Ok, I thought it was an easy thing, when you had it in View route screen.
I've tested the iPhone technique and adding to home screen. It's working great with Chrome, although I have to put the Route edit screen for a specific route to home screen. I can then select My routes in menu and choose another route.
What mobile device have you got Peter? You can do this on iPhones by adding the route planner link to your Home Screen and launching it from there. There is no way for us to programmatically invoke full-screen mode on iPhones though, so we couldn't add a button for this as it wouldn't function on all devices.
I really would like to use full screen on my mobile while editing routes. Maybe like the full screen button in View route page.