Lan never really "wanted" anything but to fulfill his duty which he see as dying in the fight against the shadow. Lan's entire life had been about loss, misery and battle. Lan never really thought about a "life after Tarmon Gaidon". Lan always figured he'd die in battle and follow the fate of his people. Given that the Shadow was defeated again and peace restored, he's kind of at a loss for what to do and since he had always been stoic and accepting of his cruel fate he needs the help of people around him to relax and get some of that Two River's lovin' and rebuild his people as the Aan'allein. I can't imagine a cushier job than king of an already well ordered and honorable people (but maybe I'm being obtuse).
I don't think Nynaeve cares about boss status. She cares about doing the right thing and the first part of her arc is learning that she isn't the Wisdom anymore and that she has to learn how to interact with the kids she was groomed to care for and guide as peers instead of as subordinates.
Thing about Nynaeve is, is she's an insufferable female dog for most of the series until she get's that Malkier shlong thrown in her. Nynaeve isn't really happy about anything and why should she be with all that pent up sexual frustration? Like Lan, all she has known is misery, loss and duty. She cares deeply for Two Rivers kids who get swept away by fate and sees it as her duty to protect them. And she's failing. Not just failing, but she's also getting caught up in the same current the kids she's trying to protect are caught up in.
So first Nynaeve tramps off to try to save to kids, but fails because she begrudgingly accepts that it's the necessary path. Then she decides she'll protect the kids on this path, by becoming a powerful Aes Sedai, all the while the kids she's trying to protect are outpacing her and she's struggling to work through her block to saidar and her unrequited love in Lan.
Lan, this dark, alluring stranger who makes her feel things she never felt before and the whole time she's struggling with hints that he likes her too, but he keeps putting her off telling her shit like, "I love you baby, but I just can't do it. My fate is to die in battle. I won't do that to you." How frustrating right? And she deals with this for like 8 books or something! And then there is the whole Myrelle thing...
But I love how Nynaeve develops once she's finally with Lan. We get to see her being reasonable and more clearheaded, because at the end of the day Nynaeve is actually an incredibly awesome character and is totally wifey/queen material.
I don't know about riding off into the sunset and leading the life of a protagonist of a western series and you may have a point about the irreconcilable tone. Personally, I'm happy for Lan and Nynave. If the series were finished by someone today Lan might turn into a rudderless drunk who picks fights with people for no reason and Nynaeve just goes back to being an exceptional nagger.
But this is a fantasy series with a happy ending. It's nice to see someone who was willing to die doing the right thing get a fairy tale ending. Egwene on the otherhand...