This is like the argument from male managers who say they can't have 1-1s with their female workers. It's tired, and shows a lot about your character.
When you say this, you're sending up a red flag with a flare.
When you say this, you're sending up a red flag with a flare.
If you won't have one-on-ones over issues that are personal and sensitive, and force them to be dealt with “in an open office with plenty of witnesses”, then, yeah, there will probably be things you can be accused of on that basis alone.
What sort of problems? I don't hear about many cases of women accusing other women of using their status as manager for sexual harassment.