Just as any sister is treated with proper deference as an Aes Sedai by the most legendary & accomplished Warder alive. The shawl is the commission. The Warders might not be directly subordinate troops, but they are partners in the fight. A junior partner is still a partner, even if he effectively has no real authority over the other. An Accepted is not remotely in this category.

But it is a similar issue to that encountered by Siuan & Leane after their stilling and then Healing. People OUTSIDE the system, even if they are kept in the dark in certain areas regarding the Power and secrets reserved for initiates, are generally treated in a more equal fashion, or at least dealt with as a adults, if lower ranking ones. An Aes Sedai might deal with an outsider as a CEO deals with a janitor on the factory floor, but there is still a certain recognition of individual adult status on some level. For people with a place in the Tower's hierarchy, if you are under them, you ARE under them, no two ways about it. Where an Aes Sedai must ask outsiders, and even if the outsider will obey or regret it 99 times out of 100, she still asks, whereas in that same situation with an Accepted, she has but to command and the Accepted obeys.

Being part of the Tower does not give you any sort of insider credibility or equality with Aes Sedai at all, unless you are part of the Tower that is allowed to wear the shawl. All being a part of the system does is slot you firmly into your assigned place. Outsiders escape that. While they might be closed off from the highest levels of Aes Sedai respect or equal treatment, so are most sisters, who are forced to defer to one another according to the hierarchy. Yet, Nynaeve has no authority over Daigian's Warder and would face extreme disapproval, if not penance for any such presumption. I see your point in that Warders are not like NCOs because NCOs & COs are members of the same group and hierarchy. However, in the case of the White Tower (note that the US Military, which RJ understood from the inside, was an organization created by males, for males, while the White Tower is one created by females, for females, which may account for certain aspects being nearly similar and absolutely opposite at the same time - Rand notes the same thing about saidar & saidin), being outside the Tower, while limiting in some aspects, is liberating in others. Because they are not truly part of the Tower (and thus their facilities on Tower grounds would be roughly equivalent to a company day care center on the premises of the corporate HQ and not appearing at all on the org chart), each Warder's relationship is a PERSONAL compact between his Aes Sedai. The terms of their relationship are akin to a marriage in that they are what the parties involved agree upon between themselves. While a Sergeant First Class or Sgt Major HAS to obey a 2nd Lieutenant, for the good of the organization, the Lieutenant's wife, or civilian tennis partner or civilian plumber is in no way obligated to the same sort of subordination. Where Egwene might feel obligated to put down Bode Cauthon for the good of the organization they both serve, Gawyn is not a part of that, his relationship or dealings with Egwene have nothing to do with the organization, the organization is explicitly prohibited from taking notice of their relationship, and he has about as much of an obligation to obey Egwene as she did to obey and show respect to Rand al'Thor. And a stronger case could be made for the latter, since for most of their time together in WoT, Rand is the ruler of the Wise Ones, to whom Egwene is sworn obedience. While she might not be directly sworn to him, her relationship with him would be roughly akin to that of a Warder to the Amyrlin Seat - only Egwene is not the Amyrlin in this equation. Let us also recall that he was the liege lord of Moiraine, who was also Egwene's superior in the Tower. Even setting aside the issue of the Dragon Reborn, of whom Davram Bashere says "the world must follow you or fail", Rand is the superior of Egwene's superiors in more ways than one. You think she would recall this, as well as his generally benign and helpful treatment of her in that situation, when she is dealing with subordinates herself. Even if we stipulate why she cannot permit Bode Cauthon the same leeway Rand afforded her, that rule does not apply to Gawyn who is in no way required to be her subordinate. Egwene herself guesses that his own sister has bonded Rand, yet there is plainly no subordination or deference there (just, you know, positive attitudes towards one another, and actual offspring, which is the point of marriage/sexual commitment in the first place).