The main issue is in the latter part of your paragraph: the organization is actually not forbidden from criticizing her choice to keep him around because he was denying that he was part of it. It actually was commented on and was a point of criticism against her that she kept him around and he was trying to act as her Warder, but had not taken the official role a Warder would take. This is why I said Gawyn wanted to have his cake and eat it, too. I see your point - I am just pointing out that Gawyn himself was confused and fighting against the role he would inhabit. At the end of the day, Gawyn wanted to fill this function, but his whole character arc was about accepting it and finding peace with his choice. As he said, he always thought he'd be leading armies and gaining glory, not serving and being secondary to one woman. If you were to critique her on anything, I would think it should be that she (more like they) made it a condition of their relationship that he would be her Warder and would have to serve in this secondary role. The truth is that they could have come to some other arrangement, but he would not be able to accompany her everywhere the way a Warder would have and ultimately, he would have less freedom to see her due to the demands of her position.

I didn't claim that being part of the Tower gives anyone parity with an Aes Sedai; but being a Novice and Accepted of the Tower is far different from being a high-ranking servant, Guardsman or Warder, especially for a student that for whatever reason (among them being intelligence, judgment, subtlety, strength in saidar, leadership ability and etc.) is generally understood amongst the Sisters to be a natural candidate for the test for the shawl. This is because the Novices and Accepted represent the future of the Tower. A Warder, Guardsman and Mistress of the Kitchens are, at the end of the day, expendable and not as essential to the organization. They serve the Tower in the way nuns, the Swiss Guard and various offices occupied by non-priests serve the Vatican.

A Warder's relationship with his Aes Sedai may be personal, but the Warder still has a place in the overall hierarchy of the organization. Put it this way: in the military, though wives are not part of the official hierarchy, control over their surroundings and living situation is exerted via orders that can change where their mate is based, modifications being made to government property and other indirect means of control. A general can't order a lieutenant's wife to do anything, but the general can arrange to have orders issued that re-assigns the lieutenant and his family as he sees fit. The lieutenant, if the wife is an embarrassment, may find his advancement hampered if his wife is unpopular and lacks etiquette. It may be the case that Guardsman are moreso ingrained in the hierarchy because we have seen them be ordered by random Sisters, but that doesn't mean Warders are superior to them. It really just seems to be a different type of assignment - it would be like comparing the U.S. Secret Service, which is charged with the protection of the President and senior level officials, and the military personnel that forms the Armed forces.

The Wise Ones and the Car'a'Carn are a different story altogether; their relationship flows both ways so it really isn't as simple as saying that since Egwene was trained by them, and the Wise Ones defer to Rand, that she has an imperative to do the same. She was their student, but as soon as she returned to the Tower, she was no longer subject to their demands. Her honor is in that she doesn't forget that she is indebted to them for their training and understands their way of thinking.