Whenever I informed someone that I would be leaving my job but hadn't yet informed my boss, they took it as an opportunity to dispense detailed advice on how to break it to him, often down to describing a rough script for me to follow.

Simpler explanation: many people will assume that if you tell them about something that sounds like a problem, you are looking for a solution. I think this is particularly true of men and engineers. It didn't occur to me that people could be looking for anything else (e.g. emotional comfort) until I had this explicitly pointed out to me by my first female friend.

so spending energy polishing the delivery of the message doesn't really accomplish much.

I think this is probably not true. Don't doctors spend energy polishing the delivery of life-changing messages? In my experience, the content of what people say is usually the least important part, and I think this is still a useful heuristic even in situations where it seems like the content ought to be the dominant concern.