However, your own answer clearly lists the evolved purpose of that nerve - it was the simple and straight line from brain past the heart to the gills; and there

However, your own answer clearly lists the evolved purpose of that nerve - it was the simple and straight line from brain past the heart to the gills; and there is an obvious reason why it can't be changed - there's no direct mutation possible to route it to the other side. On the other hand, there generally are possible direct mutations that would significantly reduce any tissue/structure, so if they aren't "chosen", then that does indicate that the tissue still has some purpose (which might have no relation to the purpose it had when it first appeared).