Reason 1 for having an EHIC:
Many insurance policies only cover treatment which is not available under the EHIC provisions. e.g. the insurance might cover you for repatriation to the UK (if required) but not cover you for treatment for your broken leg. (Insurers quite reasonably expect travellers to make sure that they've got the free - or reduced rate - cover which their EU citizenship entitles them too).
Reason 2 for having an EHIC:
It provides IMMEDIATE cover. For example, if you're taken to hospital with a broken leg, you'll be given a bill which you must pay before you leave. If you produce your EHIC that bill will automatically be waived (assuming that the locals get free treatment). Otherwise you must pay the bill and then try to claim the money back from your insurer when you return to the UK. (That could leave you having to find hundreds, or thousands, of pounds to pay for your treatment. As above, the insurer might then refuse to refund the money on the grounds that you should have had your EHIC with you).
I would never consider travelling within the EU without my EHIC (which never leaves my wallet) but I hardly ever bother with insurance.
Chris