I guess I also think that the old alignment definitions are "correct". The word chaotic means "completely lacking order" and not "values freedom". The word lawful means "obeys the law" and not "is trustworthy and obeys legitimate authority". By the correct definitions of these words, they are mutually exclusive.
The problem with using these definitions is, well, people are morons.
A significant portion of players, particularly inexperienced or younger players, will
automatically go to the very far end of what is permissible in any given artificial system of morality - and then start pushing. The whole "I get to play a total badass loner who follows his own rules and no one else's" power fantasy is very common.
There is nothing inherently wrong with that.
However, it doesn't work so good when trying to put together a
team or group or party. Most - and I stress
most - players eventually more or less move on (though coming back to it every once and a while is fun).
Others (20-30% based on my personal experiences) instead stay at the extreme, toning back their behavior only a little, because letting go is fun (I'm looking at you Josh). Again,
there is nothing inherently wrong with this, though it does somewhat limit the sorts of campaigns one can play in (which is why players tend to move on in the first place).
A rare few don't do either of the above, and just keep on playing the same "total badass loner action hero" person over and over again; these players can prove rather... tiring to deal with. I am unfortunate to have gamed with two people like this on a regular (not one-time) basis.
I mention all of this because your definitions, while quite reasonable on paper, run into a snag. A good portion of players are going to go Chaotic "Neutral", as described above, and the more "extreme / niche / out there" the base definition for Chaotic becomes, the worse those players will behave, because the book says that's what they are supposed / allowed to do.
Like everything else in a game, it's not enough to just sit and think about how alignment
should work; you need to look at the extremes and see how players will react while at them, because that's where a significant sub-set of the player-base will immediately go.