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I've certainly had travel insurance that required an EHIC when travelling in Europe. On that occasion it must have been fairly prominent. It's a few years since I got mine but I vaguely recall some instructions about what to do if the card doesn't come in time. Seeing full terms without buying the policy isn't always easy.
The benefit of EHIC varies with the destination country. It's most important for emergency treatment and having it to hand was certainly beneficial when I ended up in hospital in Ireland (I didn't end up using my travel insurance for anything despite several days in hospital).