Demanding to be the only voice would not only be impossible, it would be professional malpractice to request it. By the same token, you have never heard of a court telling its judges not to write a dissenting opinion on a case in which their opinion was in the minority. Everyone must have a voice.
Amicus curiae are critical to many non-parties because the ultimate decision could have immense implications on their businesses/lives, etc. The point, as you well know, is to give a voice to nonparties. Imagine Amarin making a deal to sell this company without the voice of its shareholders. Imagine a court making earth-moving decisions on issues like civil rights, euthanasia, immigration, etc. Without hearing the voice of those nonparties, any such a decision would/could have a devastating effect.