Browser should display a scary warning popup when submitting form to http (either always, or maybe at least when there is input type=password in a form). This would be annoying enough to get management buy-in to implement https, if someone still maintains the app - better than a tiny icon.

Breaking stuff is a last resort, nuclear option. There are many forgotten, old web apps that would totally stop working and people would switch to another, less secure browser as a result.