The E11 card is absolute crap. People go on holiday with these cards believing they are fully covered for every eventuality. The minute there is any cost involved, the card goes down the drain and the credit card take presidence over everything.
If you have to use the E11 card out of necessity you will be shipped off to the shitiest hospital imaginable, equivalent to the national health in the uk!
Anyone who's daft enough to go abroad without adequate medical insurance needs their head seeing to, imo.
And the EHIC website is pretty clear:
The EHIC may not cover persons for all medical costs incurred, so you are strongly advised to also arrange travel insurance to ensure that you are covered for all possible eventualities. Furthermore, you will not be covered by an EHIC if the main purpose of your travel is to receive medical treatment.
And the NHS is pretty good actually.