It was common in the books for other Aes Sedai to make vague references/think about Greens being a little too close to their warders. Some were even rumored to have married a warder, or all of their warders. Alanna is also often described as very fiery and otherwise emotional. She and Myrelle are referenced most often when it comes to their closeness to their warders, too, iirc.

And I'd guess it's a safe assumption that we will see some more overt relationships among some lesser characters, including more obvious "pillow friends" (which Jordan started referring to more frequently and definitively around when he put out New Spring, with a few characters outright mentioning it or thinking of such relationships they had).

I'm thinking Rafe will just make more of those things official early on and it'll allow a little more sex appeal to the audience throughout the series other than just via Mat or via Rand's relationships. It was likely to happen given Game of Thrones set a standard, and Witcher has continued it somewhat, though I don't expect WoT to be as "tawdry" overall to use your word.