Walking around in public isn't carrying the same power imbalance between a boss and subordinate that I'd mentioned.

It is simple risk aversion. A CEO has a whole world of people to have an affair with outside of his or her direct reports, and indeed company. Everyone has equal access to walk around in public. Surely this difference is obvious?

To use an example where we aren't talking about lawsuits, teachers are typically prohibited, by policy and / or law, from relations with their students before they graduate from highschool, even if the student is of legal age. There's both the power difference as well as an implicit duty of care where, even if the relationship is nominally consensual, the teacher is abusing their role as a trusted adult in power. Once the student graduates, there's no longer any official prohibition.