That's kind of the point.... Aes Sedai call themselves Aes Sedai, not "Servants of All". It's not an innocent distinction... They know the meaning of the name, but by insisting to use the Old Tongue term, they've turned it into a pure honorific/mark of status.

The Tower has turned to the common tongue for near everything it wants the people to understand. Novices have to understand what they are. Sitters are sitters, and the Hall the hall. Other terms, they've given an aura of mystery and power by keeping the OT name alone: Amyrlin, Ajah, Aes Sedai. Barely anyone, especially not the Aes Sedai, think of "servant" when they use the honorific Sedai. A great deal would be different if they'd translate the title and people high and low were calling the sisters "Servant X" or Servant of All. That might have made the AS more humble, for one thing, and become a constant reminder to them and to the people of what they really ought to be.

I agree this test goes completely against what an Aes Sedai used to be. The Accepted spend years preparing for it, and one of the consequences, though I doubt the sisters realize this, is to drive out of the future Aes Sedai all desire to be a servant of All to become a servant of the White Tower. The fact AS are servants of all is virtually kept a secret for initiates, except when the sisters have political reasons to portray themselves as "only serving". Developing a mentality of service is totally discouraged in the current Tower system, it's hardly surprising the standard test reflects this. They see such as inappropriate behaviour in a sister. Today's AS are taught to serve only when it serves the purpose of the WT and won't harm the Tower's aura of power. The average sister sees most services as demeaning for women of her status. For eg: sisters were horrified that objects crafted by their hands could be sold, sisters were angry to be seen in public working on the harbour walls. And so on.... Aes Sedai would be pissed to be forced to work at Travelling Grounds the way Elayne has the Windfinders/Kin do without a fuss. Service an AS will render with the OP is limited pretty much to fighting and healing. Almost everything else is perceived as demeaning.