With my household insurance, medical insurance, credit card insurance and the EU's EHIC insurance, why should I buy additional travel insurance?

There is a certain amount of cover afforded by those policies but it is often not complete. You must ask yourself if the cover given by those policies is as wide as you need. With credit cards, you are typically just covered for personal accident. Many of those policies don't cover adequately for the medical treatment to cope with an accident or injury.