We had a dental emergency in Germany and with the EHIC, we paid about €30, about the same as we would have paid on the NHS. If we'd gone to a private clinic in Germany (it took us a while to figure out which were private and which were the equivalent of the NHS) or paid the full cost out of pocket, it would have been a lot more.
The EHIC is great for NHS-type medical care in Europe but if you have a medical emergency and want to go private or need to be repatriated, travel insurance should cover that, as well as travel-specific issues like lost luggage and flight delays.
The EHIC is not a replacement for travel insurance.
Best plan for travelling in Europe: have the EHIC and have travel insurance.