In addition, your chance of being falsely accused is low. Your chance of being prosecuted if you are falsely accused is low. Your chance of being convicted, if you are falsely accused AND prosecuted is low. Also, the accuser's chance of being prosecuted for making the false allegation isn't that low.
We're talking about less than 100 cases per year. The real thing to be worried about is a false conviction for drugs or DUI. That happens way more often.
The impact of false accusations don't start just with prosecution. People lose jobs and friends with it before that stage. I've personally seen people fired for a mere police investigation into something much milder that was eventually dropped.
Also, I did some checking and I can't find sources supporting "100 cases per year".
Various sources say unfounded allegations are estimated to be 5-20% in different research, while there are hundreds of thousands of sexual assault cases in the US alone. This gives an estimate of multiple thousands to tens of thousands of cases per year.
I'm also not sure why you think worrying about false conviction /allegations in DUI and drugs should preclude us from worrying about something less prevalent. Can't people take precautions on all these things that threaten one's reputation and livlihood? There are many things that could have killed you with a 0.01% chance if people didn't bother to fix them, such as battery explosions, and letting them pile up because there are other things to worry about is not the way safety engineering works.
Nailed it. The amount of bandwidth men should dedicate to this is far lower than what women should be dedicating to it in terms of absolute risk.
That isn't to say you should not be thinking about making sure you don't put yourself in a situation where you could be falsely accused of something. I would say, if you are thinking in that way - spending some time making sure you don't do anything to make women uncomfortable is a good way to spend some of that energy as well - same goal, different thought process.