I don't really see Chaotic vs Lawful making a huge difference in terms of self-discipline.
If you can get a level 20 Wizard who's chaotic I can't see why it'd be such a big stretch to have a chaotic monk.
Exactly. Especially since the flavor text for the Monk at the beginning of the Monk section in the CRB says:
"These monks (so called since they adhere to ancient philosophies and strict martial disciplines) elevate their bodies to become weapons of war, from battle-minded ascetics to
self-taught brawlers."
To me, a "self-taught brawler" doesn't exactly scream 'self-discipline.' My Monk, flavor-wise, it a two-fisted brawler, not a martial artist. Granted, we don't pay a whole ton of attention to alignment, but still. I tend to play a little more toward Neutral than Lawful. Mechanically, whether you're a martial artist or a boxer, the result is the same.
I think reflavoring the Monk to make them Chaotic wouldn't take very long, just like making a Lawful Barbarian. The Rage mechanic isn't based on alignment and that's the core of the Barbarian. I do find it funny that you can be Neutral as a Barbarian, though.
Edit: Having looked over the Barbarian in the CRB, I saw nothing that says WHY a Barbarian can't be Lawful, other than 'because the book says so.'