I did notice that if your in a pvp, you can sorta use the menu chat to see what school the other player your fighting is, i think you should find a way around this because it could really change up things to not know.
Honestly I don't think it will change much, you can sort of tell on the person's name, color or their gear or design on their gear and the pet they have equipped. I never use the "menu chat trick" to see the school, it makes it sort of obvious for the reasons above.
where it is useful is when you are in team play; you might not be familiar with your entire team so it is helpful to see what schools your team mates are.
with so many different options to mix things up (secondary schools, pet spells, list goes on) the Icon can give a hint of what you may be facing but doesn't give away any strategy in stat/deck set. and if they are using a transformation, it masks a school amulet so you never know what might be coming.