The point of the mentor system is so that new players and returners can quickly identify veteran players who can answer their questions.
Mentors invite new players to the novice network regularly and returners get invited automatically after being away for 45 days or more. They regularly ask very basic questions such as how to get a chocobo, how to unlock flying or how to get better gear. Sometimes they ask for help with their queue because it's taking an hour. Mentors work together to tackle problems they have such as a quest not showing or a missing item as well.
They could use google, but it does not always yield a clear answer and a lot of people just want to play a game casually and for it to be intuitive instead of googling everything. It's difficult for an MMO to be intuitive because they are so big, so the novice network is a way for it to be intuitive by having veteran players explain it.
I do wonder why it's a crown but the crown is effective at conveying to a new player that "I don't have this symbol so they must be a veteran player". I can't speak for trade mentors but most pve mentors have played for at least a year. Even though you can meet the requirements by doing a single dungeon I think that most people get it naturally from doing roulettes and leveling all of the classes. If you look at most pve mentors they have leveled a lot of classes and obviously do a lot of content.
The role quests may be easy but they could be a lot easier. I think there are some things they do to test your basic knowledge, such as getting tanks to interrupt or healers to heal so that the duty doesn't fail. I feel sure that there are people who fail them because they didn't give any attention to the casts.
I don't know a lot about WoW, but I heard they did include their own version of the mentor system recently.
