A primary reason for having a Character Trait is to exemplify what a character is, and provide that character a means to gain Artha. That is how I understand it. However, so many of the traits that I have looked at I’m not certain that I can find a lot of ways that they would fulfill the requirement that they advance the story in an unforeseen way or give the character an obstacle. While there were a number of traits that jumped out at me when I was looking through, the one that comes to mind is Educated. I’m wondering if I am missing a part of the Character Trait system, or if some just are unlikely to provide Artha.
Some character traits may require a context for them to be useful in this way. For example, let’s say your PC with “Educated” is trying not to stand out in a crowd of uneducated peasants/seamen/whowever. Or maybe he finds himself needing to bargain/DOW or engage in a social test with someone who has nothing but contempt for ‘book-larnin’". He thinks he’s going to impress the other guy with his knowledge-- but it backfires.
Another (related) way in which these can come out is in determining failure consequences. Take a look at a character’s traits to see if any of them suggest interesting failure consequences for a given test. Sometimes a trait like “Educated” can be a source of inspiration for a really fun and appropriate failure.
In a medieval European world, the educated man is rare. Literacy is unusual. That education more or less shouts what class of person you are.
The traits and how likely they are to reward artha is not balanced no, some traits are much easier to play to. If you’re looking for artha rewards from traits pick the ones that sound like flaws. While others give you bonuses or make you cool, reflect your character etc.
Also as far as I understand artha reward from traits are pretty rare (it is the strictest paragraph of the lot). To me traits are more to help me get in character than part of the artha system.
Can’t character traits that make you look cool (Disciplined, Drop Dead Gorgeous, etc.) be used as justification to lobby for advantage?
Sure can Katsue, anything can be used to lobby for advantage. 
For character traits though, just don’t make it too much of a habit. Since that would make it more of a die trait than a character trait. Doing it is a good way to convince the group to upgrade your gorgeous(etc) the next trait vote though.