Would the certificate really help you here though? If we look back at most of the big data breaches over the last few years then we regularly find out long after it's happened. It's generally a news story or a headline somewhere that xyz company was hacked.

I see what you're saying but I can't see where this would happen whilst the user has the browser window open showing EV information. If Twitter leaks your data you'd likely get an email notifying you or watch it on the news and then take action as a result of that.