Bouncing into the middle of a long thread straight from the OP:
CG classically is a "Commit random acts of kindness and senseless deeds of beauty" orientation.
So far, so good.
PCs like CG because it allows them to commit Evil deeds (kill intelligent beings and/or steal their stuff) while in the service of a good outcome in the end.
This I strongly object to on several grounds. First, it belongs to the hideous bias that chaotic is a conditional that makes something less good, while lawful is something that makes something more good. Thus, in this construction Lawful Good is more good than Chaotic Good, and Lawful Evil is more good than Chaotic Evil. This I reject entirely. Both Chaotic and Lawful are equally concerned with good and evil, and so Lawful Good is all other things being equal no more good or less good than Chaotic Good. Chaotic Good is not a pass that lets you occasionally be evil.
Secondly, by your construction, Chaotic Good is differing from Chaotic Evil only by some relative degree and not some difference in kind. Basically, you've asserted that Chaotic Good gives you a certain number of passes to be evil while Chaotic Evil gives you more passes to be evil. But you haven't really said how much, so you could also argue that as long as you thought you were doing things "for the greater good" that you could do exactly what Chaotic Evil would do and yet on the net you would be Chaotic Good.
And thirdly, perhaps most surprisingly, this justification of "for the greater good" is exactly the same justification that Lawful Evil would make for committing acts of evil. A Lawful Evil PC could (and I will argue would) claim that murder and theft could be justified if the net result of his acts brought success (and weal of some sort) for his people. Thus, for example, a LE character might argue that his theft and murder was justified because in the end it would benefit his family, his community or his nation. And this perspective is actually entirely the opposite of the perspective of CG, because - since Chaotic is all about individualism and freedom - committing evil acts against individuals in the name of "the greater good" is from the perspective of CG exactly what is wrong with the world and exactly what CG will claim is the basis of evil - the dehumanization of individuals by assigning them collective identities.
So, no, that is not what CG is about and indeed in many ways is it's opposite.
Chaotic Good is good where the individual's own conscious and reason, and the circumstances of the moment, and the needs of the individual are allowed to outweigh any set of rigid rules regarding how to behave. In other words, it's a philosophy that bases itself around acts of compassion and mercy between individuals, rather than around a set of defined duties and moral codes. From the perspective of LG, this is dangerous because the individual will be tempted to justify acts of selfishness and self-serving acts of evil as Good - just as you have done when trying to argue that CG allows you to commit murder or theft if it is in a good cause. This shouldn't be surprising, because LG naturally considers both LE and CG to have departed more or less equally from the righteous path. CG on the other hand looking at LG, argues that having a limited and rigid set of duties allows LG to argue its way out of committing acts of goodness because it's already done 'enough' according to its moral code, and further that it has the core philosophy it sees underlying evil, that is the dehumanization of individuals by representing them as members of a collective - whether it be 'citizens', 'fathers', 'soldiers', 'women', 'children' or what not.
So in practice, CG is actually among the least, and perhaps
the least likely of any moral philosophy on the great wheel to justify killing an intelligent being and taking their stuff, because they don't see beings according to classifications but as individuals. A CG individual is not going to be inclined to prejudge anything according to appearances or norms, and will require some sort of proof that the individual beings in question have committed crimes worthy of death and are unrepentant about it before exacting any sort of penalty. Indeed, most CG individuals are going to err on the side of only killing in self-defense and will err on the side of assuming that the individuals they are confronting are only violent in self-defense (that is, they will tend to see themselves as trespassers, and the individuals they are facing have the same rights of self-defense that they would have in the same situation).
CG alignment then serves as an 'escape hatch'.
I agree that CG serves as an 'escape hatch', but I don't agree that it is the one you've identified. What CG allows a PC to do is not have any accountability to anyone but themselves. In other words, as a person that is CG, they are not under any obligation to have their actions reviewed by some superior, external judge. They are accountable mostly or entirely to the dictates of their own consciousness. Since most players hate feeling like they are constrained by any sort of rules, being able to decide for yourself what is good and right is liberating (and since freedom and liberation are really CG virtues this is really unsurprising).
Of course, if this self-centeredness in deciding what is right and wrong becomes too self-centered, either by being too passive ("I am not required to make any self-sacrifices to do good.") or too self-centered ("I am not required to consider at all what anyone else considers good, including even the target of my actions"), then that is Chaotic Neutral, since the ultimate end of such a philosophy would be that there is no such thing as right and wrong, only personal codes individuals have constructed on their own authority. And what I find in play is usually that a large percentage of people who write down CG actually want to play CN, while a large percentage of those that write down CN actually want to play CE. That is, they want to play CN as giving them a license to commit evil when it is to their benefit, and typically they'll see it as being to their benefit all the time, and their justification for this being "good" will typically only be that it is for some abstract "greater good" - which will eventually drag them all the way to neutral evil if they aren't careful.
