I don't know if this has been confirmed by anyone with authority, but there is evidence that the switch was intentional. The first part of this evidence is the interdependence between male and female in the story, then some specific evidence from how severing is healed that convinces me of the switch being on purpose.
Relationships between men and women (not limited to romantic) are important to the WoT plot throughout. Especially interdependence is emphasized, based on the number of times the story reminds us that the greatest works of Aes Sedai were accomplished with men and women working together. This could be reduced just to the ability to expand circles to 72, but I don't find that to be a very satisfying answer. There are many reasons to think that the Saidin/Saidar combination is more important than just increased power from linking:
- The creator has both driving the world.
- Elayne and Rand use very different methods to extinguish fire, suggesting that Saidin and Saidar work very differently, and using both tools will produce a more versatile skill set than one alone (also see traveling).
- Cooperation between men and women in the Age of Legends is used enough that Mierin Eronaile and her colleagues attempt to find a different source to make it easier.
- Key evidence: Rand needs both Saidin and Saidar to cleanse Saidin, and he likewise needs both Saidin and Saidar to mend the bore. The taint from Lews Therin's approach is solved by Rand using the True Power to buffer the Dark One from contact with the One Power, but the Saidin-only mend was just a patch, a temporary closure, while Rand using Saidin and Saidar together was able to restore it to something near its original state.
OK, all of that is necessary, but not really the point. Here it is:
First is the observation that women dealing with men is similar to women dealing with Saidar. Moiraine dealing with Rand is the key exhibit, but although I don't have any specific examples I can point to, I feel like this is observed by other female channelers, but only ever in reference to dealing with men, never with other women (please correct me if I'm wrong here). This starts to beg the question: is Saidar "the female half" of the One Power because it is female in nature, or because females can touch it?
What convinced me, however, was Nynaeve's healings of Logain and Siuan/Leane, paired with Damer Flinn's healings of stilled Aes Sedai. When Nynaeve used Saidar to heal Logain, he is described as having all his former power, while Siuan and Leane are left with a fraction of their former strength. Likewise, Flinn's healed Aes Sedai are described as being healed to full strength. Per the Wiki, Jordan confirmed that the opposite-gender healing played a role in this.
However, long before ever looking on the internet for an answer, I was bothered about the implications of this. Nynaeve describes her healing as creating a bridge. She feels something cut, but she doesn't heal the cut like she would a flesh wound. Nowhere else is Healing described as just a Saidar or Saidin patch. Only here is the healing described as what it is: it is a Saidar bridge that allows Logain to channel Saidin.
Do all men who channel walk around with a bit of Saidar in them? Do all women who channel walk around with a bit of Saidin? That also explains Siuan and Leane - their now Saidar bridges are a poor imitation of the original bit of Saidin that allowed them to channel in the first place.
You mentioned that the dots are missing, the dots that represent the seed of Yin in Yang and the seed of Yang in Yin. In your link, it seems that Jordan meant the omission to be a sign of the disharmony between the two halves. The symbol of ancient Aes Sedai was also made by the very human Aes Sedai of the age, none of whom knew how to Heal severing. Mierin wanted to discover a way to discard the Saidin/Saidar differences and find the One Source for men and women alike, and scholars of the age seemed excited by this possibility. Even though only a few actually created the bore, there was deep and widespread misunderstanding of the nature of the One Power shared by those who created the symbol without dots.
The truth is that Saidin only works with a seed of Saidar, and Saidar only with a seed of Saidin. Again, I have to ask the question: do we call Saidar the female half because it is female in nature, or because it is wielded by female channelers?
Of course, the simplest answer could just be as commented in the OP that the dark had to represent male and the light female for other thematic reasons, but it's also possible that Jordan intentionally muddied the difference between the identities of the powers and of those who wielded those powers.