The EHIC only provides the same basic statutory care as citizens of that destination country would receive.
In an emergency situation, especially in a foreign language, the last thing you want to be doing is checking if the health care you need matches what a citizen would receive for no cost and you won’t be left out of pocket.
Consider your return
Be aware that there’s no guarantee you will be able to return home when and how you want if travel restrictions are issued.
The last few months have seen rapidly changing entry and transit restrictions and thousands of flights cancelled. If your return travel were to get cancelled and left you stranded abroad, the insurance you would usually rely on is now invalidated.