I feel the first few issues can be greatly alleviated by simply taking those issues seriously, making it known that kind of behavior simply isn't tolerated, and following through if those things ever come up. That last one is the key, there. I don't know any workplace that doesn't say they take those things seriously, but actions speak louder than words, and if you're not prepared to terminate people who behave in that manner, then you're not taking it seriously.
I've tried it both ways, and I definitely find it easier to lead people in person. I learn so much from implicit communication in person that has to become carefully explicit when remote.
I also think the sexual assaults thing is a terrible red herring. Remote teams still should get together regularly, and abusers will happily abuse then. For that matter, abusers are perfectly capable of being abusive remotely. (Exhibit A: the internet.)
Working from home can make a manager feel less control. It takes a different type of leadership. But requires less leadership points.