As it is, I generally do not believe that Law and Chaos are not simply troublesome little remnants from ye olden days of D&D.
Many will agree that alignments are not always so "realistic." At times, yeah, I'll grant you that.
However, I believe a Good versus Evil scale to be more unrealistic than the four tier scale of Good-Evil, Chaos-Law. As it is, I generally find the ethical (Chaos-Neutrality-Lawfulness) to help better represent those actions which do not coincide with the moral (Good-Neutral-Evil) aspect of alignment, and vice versa. Very few individuals could really fall under the heading of just Good, or just Evil. But, by granting them another personality and motive descriptor, it helps loosen up (in my opinion; one could say it's more restrictive, but, I'll go into why I think the way I do) the alignment they wear. A Good character may do something morally questionable; however, if the individual is Lawful Good, and the act is ostensibly Lawful if not Good, then the act becomes a little more acceptable. Note that this isn't quite the case with paladins, where both parts of their alignment only serve as a greater restriction (and not necessarily a bad one, mind you).
As I see it, the two aspects of alignment better describe, as much as one can apply alignment to a world that isn't black and white, the personality and the way people tend to act. At least, better than anything so ambiguous as Good and Evil would. That's more simplistic than I care to bother with. At that point I'd say you'd be better off just discarding the alignment system. In my Scarred Lands game, the battle of Chaos versus Law has almost become the most prominent of alignment conflicts. Yet, by that same token, the one between Good and Evil has also cropped up to a degree (possibly a bit more on an internal level for at least one character, but there you have it).
Chaos and Law may not play an important part in some peoples games, but it serves a purpose in a good chunk of them.