> they need someone to initiate the interaction, and they need to know the rules of the interaction, since this is mainly the reason they don't feel comfortable with freeform interactions with strangers and so avoid them.

You hit the nail on the head with the above.

It's why things like square dancing where so popular back in the day.

It gave men and women an easy to learn, simple to follow set of rules for interacting with the opposite sex with as little ambiguity as possible. e.g someone was literally calling out what to do next so you could enjoy the moment rather than thinking "oh no, I'm not sure what to do next!"