An evil character who keeps agreements, is loyal to his comrades, etc. is a lawful evil character, not chaotic evil. Lawful is to be ordered, and to honor rules and restrictions, even if you use them to selfish or evil ends (such as extracting a vow from a paladin under false pretenses). Chaotic is to give such things no value. Chaotic characters are not bound to keep thier word unless it suits them on the particular day. Nor does authority have any special meaning to them.
I can imagine playing a lawful evil PC in a good party. One need merely have an agreement with the party that the evil PC will honor and the other good PCs are comfortable with. I find it much more difficult to envision a chaotic evil PC working out
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What you are describing is what I call "Chaotic Dumb" -- a person who is so out-of-control that they are the own worst enemy. Such a villain wouldn't last 5 minutes unless he had a lot of power and even then his life-expectancy is rather low. It also makes for a villain would is little more than a stereotype. For example, how could subtle demonic creatures like Succubae exist and be effective when they would otherwise give themselves away so quickly? Meanwhile, by comparison, Lawful Evil has a wide range of possible playing approaches. One is a dead end; one is really the only sort of alignment that makes sense for a long-term villain.
This is me illustrates the long term BIAS that has existed toward Chaotic alignments and in favor of Lawful ones since the inception of the alignment system. Basically, I see it as a likely manifestation of the creators' own biases writ large.
As is implied in the description and from what can be seen in similar personality patterns in real life Lawful characters define "structure" in their lives primarily using >external< factors such as laws and social customs. They tend to work toward living out these collective assumptions in a way that verifies and gives them meaning. For example, take a look at the military -- it operates under a set of "rules" that every soldier is expected to obey. Those rules exist outside an individual's own personal determination and dovetail nicely with social and cultural expectations. To a Lawful person the law exists because people give it life by abiding its dictates.
Now, to a Lawful person those people at the other end of the spectrum (which we'll call here "chaotic") seem to not have any structure to their lives. They may in fact seem to flaunt social expectation and otherwise act according to their own (apparently idiosyncratic) whims. This is where I see the Lawful bias to the alignment system -- "Chaotic" is relegated to little more than having a lack of self-restraint and/or social pride. That view is the >biased< way Lawful individuals in real life tend to pigeonhole those on the other end of the scale.
However, in truth those on the other end of the scale are apt in their own way to have just as much or little self-restraint as those who are Lawful. The difference comes in how Chaotic individuals see structure in their lives -- NOT primarily according to social and legal expectation, but rather the determination of their own >individual< understanding of the intrinsic rights and worth of other individuals. This may sound selfish or closed-minded, but again this approach can be just as good or bad in that regard as the Lawful approach.
For example, in a slavery society Lawful characters (who may not otherwise like slavery) would tend to support the institution primarily because that is the way of things. Mess with one fundamental aspect of the system and you may damage it all. However, a Chaotic (good in this case) person would likely denounce the process or at least work against it because to his mind what matters are the intrinsic rights of the individual -- even a slave -- rights that ultimately make him no more or less of value than those in charge.
A Chaotic person can likewise live a "structured" life, but that structure will come primarily from his own internally developed code of ethics -- that is, what his own experience has taught him -- rather than investing in some group ideal. As such they should be just as capable of learning supposed "lawful" abilities like those of a Monk as anyone. In fact, many if not most of the "heroes" in the movies who possess such "monk-like" abilities are clearly Chaotic in their alignment (Neo from the Matrix movies being one classic example).
I can illustrate the effects of the anti-chaotic bias in the alignment system by turning everything around and describing how it would be if the system was biased against Lawfulness. In that sort of system Lawful characters would be little more than stooges or willing accomplices to the prevailing social order -- they would have, in effect, given over any control of their lives to the directives of the state. By comparison, Chaotic individuals would have retained their abilities of self-determination and would be able to see through the lies and illusions of the ruling elite.
A more balanced approach to Lawful/Chaotic as a have talked about here would make both points-of-view equally valid, both possessing their strong and weak points. It would do away with the Lawful bias of the system, illustrate that Chaotic means more than simply having no or little self-control, and make the system more in keeping with real life. And, in fact, the basis for this view is there already in the rules; it just seems that the Lawful bias regularly creeps in.
