You mistake me disputing your definition for not looking at the big picture.
https://www.merriam-webster.com/dictionary/mouthpiece
a : one that expresses or interprets another's views : spokesman
"I come bearing an offer from High King Anduin Wr--"
What ever, Allerias agenda is, she was passing on a message from Anduin in the moment. If her motivations her own she could have pitched Quel'thalas joining the Alliance completely differently, but no she took spokesman for the Alliance angle.
I don't think anyone was ever suggesting Alleria has no agenda of her own. I think at the end of the day it's more of a criticism of Blizzards writing, the Alleria that we know, the Alleria that loves Quel'thalas and her people would not have just come as some one puppet.
The obvious answer is Blizzard wants Horde players to dislike Alleria, they want her to seem like this poacher trying to steal the Blood elves from the Horde. However the character they picked was once a proud Quel'thalas nationalist, making the whole ordeal cringe-worthy at best, and another clear attempt to throw more fuel on the faction conflict.
So no excuse my "naughty and edginess" but the notion that Alleria is conveying herself as anything but Anduin's lap dog in that quote is bullshit.