When we first hear that Laeshana wants to become an orah, it seems like it's just a desire to access all four elements, instead of being limited to her native fire. However, a new reason becomes apparent when you read her description of how there's dark magic all tied up in her fire magic, and how she constantly has to fight to keep it under control, and you remember that orahs "live aligned with light alone", and alone among mages have no darkness to their powers. Even if she didn't get the other three elements, just being able to use fire without having to constantly fight the lure of dark magic would be unspeakably joyful.
Laeshana's anger at being dismissed as a "superstitious peasant" by Ruahkini makes a lot more sense if you have read the background material and know that graduates of the College of Magic (such as Laeshana) are the social equal of Caederian nobility in most circles.
If Alaric doesn't complete his quest, there will be civil war. Now just imagine what civil war would look like in a country ruled by mages. Mountain ranges flattened and raised up as obstacles, entire counties blanketed by week-long or even month-long thunderstorms, rivers wrenched out of their course to wash away armies, wildfires sufficient to reduce cities to ash, the Trace turned entirely towards weapons of war, having to worry every moment about a ruahk or even unaligned assassin popping out of thin air to slit your throat, the aretzes being drained dry trying to keep up with war injuries, shamais calling on their power to turn or subvert prisoners, and peasants caught up in the middle of it all with no way to defend themselves.