For many of the reasons you list, Elayne is in a superlative position. An argument could be made that SHE is the most powerful woman in the world (or has the greatest potential power), and not the Amyrlin Seat. This places her in the best position to break the supremacy of the Tower over the wetlands and put it in its proper place as no more than an equal polity, and maybe even first among equals socially, but not exercising any authority or influence over the governance of any land save that of a peer and neighbor. Elayne is an Aes Sedai which gives her a personal basis for defying sisters and the Tower such as rulers have dreamed of for three thousand years. What is more, she came to that status under highly unusual circumstances and lack the years of being molded into a devotee of the White Tower that other rulers who have worn the shawl openly or secretly have received. Beyond that, look at her advantages (the Seanchan being a possible exception to all superlatives, of course):
- She rules the most powerful nation in the wetlands in her own right
- She has been accepted as the ruler of the sole significant rival to Andor (her other neighbors lacking power or size and other nations of similar power being too remote)
- Her domains are the keystones in a nascent network of allied nations
- She controls the most advanced military technology in the world, with the dragons, an alliance with the Two Rivers longbowmen [RJ & B-Sand have not by a long shot come close to giving an idea of the rarity and utility of that skill], and control over both academies and access to the technology seen in development there (steamwagons, repeating crossbows, optical technology, nascent flight and powered ships)
- She is allied to the best organized and most professional military organizations in the world, stated in the BWB to be the Children of the Light and the Band of the Red Hand, which now works for her second only to her Warder and the father of her children. It is almost inconceivable that EITHER of those groups could ever support the hegemony of the White Tower or betray Elayne or Andor to the Tower. Particularly in light of the idiosyncrasies of their commanders.
- She is partnered with a channeling organization. While that group is currently the least of all such groups in the world, they are the only one with financial incentives and free market inclinations and thus have the greatest potential for growth.
- Aside from Rand al'Thor, she has the closest relationship of ANY ruler with the foreign cultures and their advantageous specialties.
- As far as the impending Last Battle will impact the geopolitical situation, Elayne uniquely has official working relationships of one variety or another with all three of the ta'veren who will be responsible for the outcome.

And where are all of these advantages placed? In the hands of a woman who will not turn against Egwene for ANYTHING. Elayne almost always chooses loyalty to her friends over her duties. Her acquiescence to the Wise One's requirements for her adoption of Aviendha, her appointments of Birgitte as Captain-General, Nynaeve as her Aes Sedai advisor (a position of public, formal significance in Andor, unlike most other nations), and Thom as official court bard, regardless of their issues that might render them unfit for the job or political embarrassments (a blanket pardon issued to the murderer of the last ruler of Cairhien right before claiming the throne herself outweighs even Nynaeve's & Birgitte's aversions to diplomacy or public decorum), and grants them extreme latitude in their attention to those offices as well as her brothers' divided loyalties. She pursues a relationship with Rand regardless of the possible costs to her political career or opposition from personal authority figures or the difficulties he has created for her claim. She lies to Aes Sedai, whom she has been raised to revere, for his sake, views the Tower split for how it can be turned to Rand's advantage and turns against Elaida who made the gardens bloom for her to play in when she shows possible hostility to Rand. When it might have been more prudent to allow Morgase to remain publicly dead, Elayne openly restores her mother to prominence. At almost every turn or point of decision Elayne comes down on the side of friendship regardless of the consequences for her country or political aspirations (though it is a testament to her ability that she manages to service the latter goals in spite of conflicts with her apparent priority).

Even worse is that she never turns on Egwene no matter what. In addition to the issues with Rand mentioned above, none of which do the slightest to dissuade her from pursuing an relationship as immediately as their circumstances and her own intimacy issues permit, she expresses a willingness to defy her mother, the woman who raised her and the expectations of her position and the Tower for Rand. She accepts, in the abstract anyway, the possibility of sharing him with other women, long before she learns the women in question will be her friends, much less acceptable partners in such a relationship. When she does get accustomed to her friends' feelings for Rand, she is open to the idea of polygamy and is arguably the strongest force for it, even more than 2 women who have prophetic certainty of its inevitability, one of whom has been raised to see it a preferable institution. For Rand she will go this far and possibly beyond. In fact, there is only ONE thing she has proven she will not do for Rand or to get a relationship with Rand (even pulling a Lanfear and turning to the Shadow has never explicitly been ruled out): turn against Egwene. She momentarily entertained the idea of tying up her oldest friend to prevent her from going to Rand, she contemplated stabbing Aviendha for admitting having slept with him (though Berelain had her sure he was already used goods), but she never once thought of pursuing him so long as Egwene had claim, however neglected, and no matter how indifferent to him Egwene showed herself. She spent several weeks under the same roof with a man she loves, and never so much as flirted with him, because he belonged to Egwene, no matter how little interest Egwene herself showed in that relationship or how much Egwene insisted he was unfit for a relationship. Min's reaction was to call bullshit on that position in a heartbeat. Aviendha felt strongly enough to give in to her feelings at least once in spite of her envisioned prior claimant actually showing interest in maintaining said claim, and their close mutual friend's disapproval. Elayne? Where Egwene is concerned, she waits her turn. Are we supposed to believe she'll do what is necessary to move the world out from beneath the stifling influence of the White Tower as long as Egwene sits on the Amyrlin Seat?