Sorry to burst your bubble, but this has actually happened. The case I know of, personally, involved a bar owner. He was exonerated after a few years being dragged through the mud, but he ended up having to shut down his bar and move out of town to be left alone. This stuff happens.
Do I have a better alternative? No, it's a complex issue and we definitely don't want to victim blame, but we also don't want to destroy people's lives over just allegations. It's a delicate balance. I think one thing we could do, at very least, is to actually stand by the innocent until proven guilty ideal and not publish the identity of the accused until a verdict comes out. This is the way it is in most of Europe and a "perp walk" happening like it does in the US would free highly illegal.
I've given a lot of thought to this issue in the past and I think it all boils down to one indisputable fact:
"You just believe her" is completely at odds with "innocent until proven guilty."
"We should believe women" is a laudable phrase, and it makes us feel good to say it, but men are victims as well, especially trans men. "We should believe victims" would be better, but it is a begging-the-question fallacy, it assumes the victimhood is true. The people who made that not possible are specifically the people who have made false allegations in the past.
It is far, far more common for women who allege to be completely ignored, ridiculed, dragged through the mud should they choose to pursue charges. That's a simple fact of the world. RAPE IS A BIGGER PROBLEM THAN FALSE RAPE ACCUSATIONS.
I'm not denying what you're saying, I'm saying both are a problem and advocating for not throwing out the baby with the bath water. There must be a way to adjust our system to account for both cases, no? Or would that be objectionable to you somehow?