I find it interesting that we never seem to hear the other side of this coin.
Stripped of all other issues, Brexit will see the EU lose 17% of its GDP and 8% of its income. Depending on the trade deals, Brexit might affect the UK's economy, by making it harder to export stuff and more expensive to import stuff, but it will directly affect the EU's by slashing its value by a sixth and losing nearly a tenth of its income* overnight. If Brexit happens, that will happen regardless of any other considerations.
If everyone keeps going Hard Brexit, No Deal, the EU will lose access to seamless free-trade with its third largest export market (after USA and China) and second largest supplier (after China)** of goods and services - and, worse still, the UK is the number one supplier of financial services (something the EU cannot move without considerable expense, running into the billions with ease). That will then make it more expensive for EU citizens and businesses to get money - which could be a catastrophe for Eurozone countries already struggling economically, like Italy.
On that basis, rather than the EU being immovable on the grounds of punishing us for leaving and discouraging anyone else from doing the same, it might simply be a tactic to make Brexit look as awful as possible to hope it's overturned by popular vote because it will be devastating to the EU. Once it's inevitable it simply won't be in the EU's interests to stick to its guns on trading with the UK, because the direct and unavoidable effects of the UK leaving are already bad enough. It's going to have to budge once Brexit is inevitable, or risk damaging itself so much that, regardless of the bad deal for the UK meant to dissuade other nations from leaving, other nations have to leave or face collapse.
*Although I recall something about the contributions not stopping immediately, rather tapering off over three-ish years.
**Outside the EU27; Within the EU28, Germany is the largest exporter and importer, but once out of the EU28, the UK will become the third largest customer and second largest supplier.