I don't think Jordan was all that interested in showing people falling in love so much as exploring what it's like to be a relationship in these situations. A lot of fantasy has a prince charming or the hero getting the princess, right at the end of the story, so what's it actually like to be married to a noblewoman from a badass family, or the heir to a throne or the heir to the Evil Empire or the heroic dispossessed king or a charming prince who is good hearted and devoted to the women in his family? Perrin is having to cope with a wife who has expectations for how a leader is supposed to act and how a husband who is a leader is supposed to behave and what marriage between leaders entails. Min has to deal with having a subordinate place in Rand's life due to the demands of his prophesied duty and has to watch him suffer to save the world. Mat can't simply reform the Evil Empire because the new Empress is his wife, even if she likes and respects him. Gawyn's devotion to his female relatives puts him at odds with Egwene and her loyalties. Lan's royal status traps him until there is almost no way he can see to pursue a relationship with Nynaeve. And politics can put Elayne and Rand at odds, regardless of their shared beliefs and similar agendas, while other duties separate them. That small amount of time they have together is, I think, an intended feature of their relationship arc (though I think the story did get away from Jordan a bit, and it wasn't supposed to be quite so long, or their time together was intended to be such a small portion of the story). I wouldn't say the lack of opportunities for physical intimacy diminish the relationship, since both of them make rather serious choices due to their feelings for each other. They are a lot more alike than either is to Aviendha or Min, and honestly, the most alike of any of the major couples, with Mat & Tuon coming closest, though with a much greater cultural and social gap. They are both driven by duty, putting it ahead of even their own well-being or wishes, both consider their own personal desires selfish and unworthy of consideration next to their duties (though Elayne is much better at handling the work-life balance) and both share with their brother a hard-line perspective on right and wrong, however willing to make necessary compromises for the greater good (which Galad is also more willing to do than he gets credit for). Narratively, I think the ta'veren driven love-at-first sight was to enable Jordan to skip the drawn out process getting to know each other past the gulf of rank and status would have been, and within the story, it was connecting two kindred spirits whose ability to work together would be critical to uniting humanity for the Last Battle (especially under an author who understood the themes of the story and saw unity & leadership as something more than political allegiance and offices). I've said elsewhere, that I think ta'veren doesn't make people fall in love so much as it helps couples overcome social constructs that would obstruct a relationship and obfuscate their personal compatibility, just as it doesn't change one's allegiance or priorities, so much as it shows why a particular leader is the best way to serve a cause you think is important, or how that leader is the right one for you, despite those same social constructs that tell you otherwise (eg Bashere & Rand).

With Elayne & Aviendha, I think the non-sexual aspect of their relationship is important to Jordan's intentions, of showing that friendship is just as significant and just as meaningful as sexual partnerships. Elayne and Aviendha's arc cannot be called anything other than a courtship. They deliberately start feeling each other out and make an effort to get to know each other, culminating in a formal commitment that was the stated goal of at least one party from the outset. It's Jordan saying that your friendships are as important as your marriage/partnership in some ways, and that sex or the lack is not the defining feature giving meaning to a relationship.
And I would put money on the show making Aviendha and Elayne lovers if the show gets that far into the story, because the fans of that dynamic fall squarely into the segment of the fandom that the writers are part of or pandering to. Judkins expressed interest in portraying Rand's relationships, though I have heard he has talked about making the polyamorous instead of polygamous and has expressed a delight in altering the sexuality of characters especially in response to objections based on their canonical status in the books. I don't know if this is just wishful thinking from the shipping fans, but I have seen people claim that Ceara Coveney and Ayoola Smart have hinted at something of that nature for their characters' arcs, and flirt with each other on social media as if promoting it.