It's true that the justices will grandstand for their egos (much like attending doctors to residents and students). But I am pretty sure that the lawyers arguing before them also have pretty strong egos. Realistically, if the issue is just presentation of information, then there is no reason at all to go with oral arguments. Everything could be written down and presented in this fashion. But - if I can tell what direction the argument is proceeding (and I know this happens when I ask residents or students to describe their reasoning about a case), I will freely interupt in order to save time, or to let them know that I have already considered and rejected their ideas. This allows them to bring in other issues that they should be prepared with.

I would be quite certain that a lawyer arguing before the Supreme Court has been challenged before, and has a variety of arguments to back up their reasoning. I assume the Justices are at least passingly familiar with the cases before them, and so have some ideas about what the argument is going to be. Asking questions lets the attorney know that this or that line of reasoning is being seen favorably or not, and to adjust their thinking "on the fly". Thus the merits of an oral argument are preserved, and unique to the oral (vs written) case. Once the argument is written out, there is really no room to adjust it, or tailor it.