Never in the US legal system are you trying to prove anyone's innocence.

So when the accuser accuses someone without any proof, and if the case is taken to the court doesn't it imply that the innocence of the accused is tested? If it isn't the case, then why take a case WITH NO PROOF to the court? Why even complain if there is no proof?

It's entirely possible that someone can be judged not guilty, yet their accuser can also be judged not guilty of false accusation.

This is the verdict given by the court but would the society accept it that way as in rape and sexual assault cases it's mostly guilty until proven.

Also there is something called as "Wonderful women effect" which suggests that people associate more positive attributes with women compared to men. This bias reflects an emotional bias towards women as a general care. So, proofs are the only thing which would lead to a judicial decision rather than the final decision influenced by this effect.

Imagine someone accused you of any other crime without ANY proof, would it be given the same consideration as this one?