Drow aren't exemplars, for, um, example. I'd further point out that it's a common but I think illogical and slightly unreasonable take that because a race has a complex social order or societal systems it cannot be individually usually Chaotic.
It's possible to have a complex social order and be Chaotic. In fact, for highly populous societies we would expect that chaotic influences would lead to a more complex social order than strictly lawful ones. The reason for this is that we'd expect a highly lawful society to produce a universal social order, but more chaotic one we'd expect to have multiple competing social orders which have arisen at least in part organically and "bottom up" through the interactions of numerous individuals. But none of those things are true of the social order of the Drow, which is "top down", universal, singular, and rather poorly rebelled against. Individuality is heavily suppressed. Rules and the overall social order are rigorously enforced. And while the society does foster competiveness and ruthlessness, nothing about that competitiveness and ruthlessness differentiates it from a lawful evil society. It's clearly evil, but the "law" and "chaos" descriptors are meaningless.
Not saying you're saying that but it's a common objection to the Drow and I feel a very weak one. Chaotic just, to me, may just mean they're not very keen on sticking to the rules...
Except, what we see in the fiction is a society which is rather keen on sticking to the rules. They may bend the letter of the law, but everyone is afraid of cheating because breaking the rules or abandoning them gives society the excuse to collectively persecute the rebel. This situation is enforced on the society top down through a feared and beloved authoritarian lawgiver.
The big problem I have with this is that it confuses the motivations of a mortal actor with an immortal actor. So suppose we have an evil society with a charismatic powerful mortal figure who is chaotic evil. That mortal figure has the motivation to organize society around themselves and so they may well desire to publically promote the values of law in order to increase the loyalty of society to them and thereby increase their personal power. The more lawful their minions, the more loyal they will be to their leader provided that the leader can present a public face of lawfulness and continue the masquerade and charade that they exemplify the lawful principles that they are teaching. And this is a very chaotic evil thing to do.
But, supposing the leader is now an immortal deity that is supposed to exemplify chaos and they have a similar motivation to increase their personal power, they cannot behave in the same manner and encourage the values of law even if doing so increases their temporal power in the short term. There are numerous reasons for this. First, to do so would be philosophically conceding that law is the best way to organize society and that organization and suppression of individuality has value. Secondly, because as an embodiment of chaos, promoting law ought to be so distasteful to them as to be actually painful. Even if the resulting society served them, the resulting society would be too distasteful to bear. As an exemplar of chaos, promoting law for chaotic ends would be as distasteful to them as promoting evil for good ends. The ends do not justify the means here. Finally, in most cosmologies this practice would actually end up decreasing the personal power of the immortal in the long run, since the majority of the chaotic evil deities followers would actually be lawful, we would upon death expect those lawful followers to end up in the camp of a different deity. The charade couldn't continue forever. All that promoting of law in the long run has consequences, in that the power of law over both life and the afterlife would increase to your detriment. Certain available facts would inherently contradict the charade. You hold over your power would be tenuous at best.
Still I do think NE would be a better average alignment based on lore, so I'm not entirely disagreeing!
Sure, but traditional Drow depictions have been centered on exclusive rule of a CE immortal, so even NE represents a bizarre departure. Where is this LE influence coming from and why does Lolth tolerate it?
The truth here I think is somewhat more simple and can be found in the meta and not the fiction. Gygax tended to have the bias that LG was "more good" or "most good" where as CE was "more evil" or "most evil". This shows me that Gygax was not fully certain where he stood on the "law" vs. "chaos" axis, especially once it had been complicated (somewhat against his wish) by the "good/evil" axis. Consider how in BD&D "law" does seem to mostly represent "good" and "chaos" mostly represents "evil", which again is a confusion compared to the source material for the "law/chaos" axis (where neutrality represented life and thus was "good" relative to mortal existence). This bias persists in other people both for the same root reasons and because of the precedent Gygax set. But modern society trends "chaotic" (individualistic) and so if you ask a modern person to imagine the "most evil" thing that they can imagine, they will almost invariably answer by describing some form of fascism and not some form of anarchy. This bias persists in Gygax as well, so having identified "CE" as the most evil thing, when describing it he ironically tended to describe it in terms of LE. And again, this confusion in presentation tends to persist in a wide number of sources, hence the LE nature of Drow society despite supposedly being a society that is universally or nearly universally CE.