I wonder if there's a way to programmatically re-generate the one-time-use codes. It might be a fun project to set something up that emails a one-time-use code to my work email and then regenerates one.
There's a massive amount of websites that are blocked, so it's not really what I would call 'unfettered.' The reason that phones aren't allowed is related to the fact that they have cameras / microphones. They don't want someone's infected phone spilling company secrets.