Insurance is a gamble, you’re gambling on something going wrong and getting a payment
NOT buying insurance is the gamble; you're gambling on something NOT going wrong and therefore not needing to get a payment to cover you in the face of potentially life-changing events and the resulting bills.
For a very small premium, e.g. as low as a few pounds on a one-week holiday to Europe, you are providing security for yourself and family in the event of something going wrong either before your holiday or during it.
The EHIC card only provides treatment at the same level as that provided to citizens of the country in which you fall ill or are injured - it does not always cover the cost of ambulance transport (or even helicopter transport), nor the cost of rescue, or repatriation, nor of rehab once you get back to the UK. All of these can add up to several thousands of pounds - if you don't buy the insurance, you're gambling that you won't need these.
Travel insurance covers other events too. As many have posted, it covers if you if you cannot make the trip due to illness or accident.
It also covers you for public liability. Imagine that you are about to cross the street and forget that traffic is coming from the other side of the road to what you are used to in the UK. You inadvertently step out in front of a cyclist, who swerves and crashes into a bollard, breaking his leg and fracturing his skull. You risk being sued for causing the accident and the impact on the cyclist's life (loss of earnings, permanent damage to his leg that prevents him from cycling, playing sports etc in the future, his medical bills and so on) which could run into many thousands of pounds, as might your legal bills. And this works both ways - travel insurance covers your legal and medical bills and supports you should you be the victim of someone else's actions.