I would, simply because of the implicit hypocrisy and sort of double-dealing and Tower-centric behavior it encourages.

The only problem with this is that Ajahs are more like organizations with a particular area of focus. They are NOT specializations of skills or divisions of labor. While the areas of interests mean that the two definitions have some overlap, and for all intents and purposes they WILL be divided up like that, it is still not the same as, for example, a military organization's branches of service (Engineering, Intelligence, Aviation, MP, etc). Thus Cadsuane, a Green, can be the premier hunter of male channelers in the world, and no one within the Tower ever comments on the apparent incongruity. That is because hunting male channelers is not the Red Ajah's JOB or specialty, but merely their area of interest, and the thing they believe to be the highest priority of the Tower.

Additionally, your proposal to assign the sisters on-going jobs based on their Ajah runs counter to the personal rights of the sisters. They are not soldiers, and the Amyrlin is not their general who can command them as such. She is more like the head of their nation, and as such has no right to dictate their lifestyle choices or career pursuits. While in both cases, such a person has a great deal of power and authority and as a practical matter can make things very unpleasant for people who do not follow her wishes, your proposal would be as contrary to the traditions and spirit of the Tower as Elaida's proposed Oath.

How so? Are they going to stay in a perpetual link all day? Another way to describe this plan would be "dissipating their strength and inviting defeat in detail."

So you are going to completely redefine the non-combatant initiates as well? Because such women would be a pure liability from the standpoint of the sisters who would not consider using novices and Accepted to fight. At most, they might bring them into links, which would not matter much. Against conventional threats, a link is overkill. Most Aes Sedai possess sufficient strength in the Power to kill a person, so they don't need more than that. A link is counter-indicated for most fights, unless they are up against more powerful channelers, who would have better options, like picking them off one at a time.

This would absolutely suck from the Tower's point of view! The Tower's training WORKS, whether or not it produces your ideal of a channeler. Your way would lead to drastic changes and alter the Tower out of recognizable shape. One of its strongest arguments and benefits is the continuity it provides and represents, and your reforms proposed thus far are dynamite placed at the foundations of that continuity.

The Tower's training first and foremost inculcates a strong, predominant loyalty to the Tower. This allows the sisters as they rise through the ranks to hold the Tower and its traditions important enough to uphold and protect them for their own sake, hence the continuity. Additionally, it makes them put the Tower first over other polities. While sisters may not put aside their national loyalties sufficiently to remain objective on issues regarding their homelands, there are few to no cases in the books of a sister actually siding with her homeland over the Tower. In your scenario, women who lacked potential might never actually set foot in the Tower! How is that loyalty which is so important to the Tower supposed to be maintained? How is nationalistic sentiment supposed to be overcome if they don't ever leave their nations? The Tower's way has even the Kin who hide form sisters professing a superior loyalty to the Tower, and thus preventing them from acting against its interests. Your way is seeding a garden of anti-Tower sentiment and rebellion.

What right does the Tower have to demand lifetime service in a manner they deem useful? Who are they to decide what is a useful function of a person's life? Why should they not have the freedom to spend their lives in ways that make THEM happy?

On what grounds? Getting the shawl is not like being fully brought into the command structure, it is a graduation. This is like forcing a graduate to work for his university upon attaining his degree. The point of getting the shawl is that now you are an Aes Sedai, legally equal to all the others. Aes Sedai are not soldiers, minions or vassals of the Tower held to it by regulations and rules and discipline, they are independant women with their own interests and agendas who gravitate to the Tower by choice and affection. This is why the Amyrlin lacks the authority to demand sisters report on their whereabouts or swear oaths of personal obediance. If the Tower was what you seem to believe it is, Elaida's proposed Oath would be a non-issue, as Hitler's equivalent demand of the German military was. The nature of their oaths of service made that oath redundant. For the Tower, however, it represents a radically different way of interaction.