Worst. Idea. Ever.
Three sentence email is the idea that all emails should be no more than three sentences long.
Email takes too long to respond to, so pledge that all emails will be answered in three sentence or less. Well if you take that pledge, I hope you are not using these emails to form or reinforce a relationship, convey a complex concept, or convince someone of a new idea.
Actually, if you are taking that pledge, I hope you’re not emailing me.