The EU is too reliant on exports to the UK to play hardball.
I think you and the UK public are mistaken. The cost of another country leaving the EU far exceeds the cost of punishing [1] GB.
Think about it. What if GB gets nice deals for nothing? I assure you that within two years the EU is over. There are many countries with a large fraction of people that are anti-EU. I think the EU will rather loosen sanctions on Russia than giving the UK a good deal. Im wondering how the US government is thinking at this very moment.
One lesson we can draw is that the EU should advertise their benefits in a better manner. And "wir schaffen das" is a sure way to blow up the continent.
1. actually punishing does mean nothing more than to give no special benefits to the UK. They had it, they will loose it.