I think the only answer is, peace of mind.
If you’re in agony or semi-conscious or even not conscious at all, you’re not going to want or be able to sit down and start googling for a suitable insurer and filling in forms on the computer. But you could argue that if you’re in that state, it’ll be classed as an emergency in any case.
I have to say I have thought along those same lines myself.
Not true, by law a mutuelle can’t turn down anyone who has a carte vitale.
Of course if you use a private insurer not a mutuelle, it’s different.
@John Alderson, have you looked for better quotes? In your position the big dilemma is, having paid in so much already and never needed to call it in, it would be sod’s law to need to call it in as soon as you cancel it - so the worst of both worlds, all that money down the drain and still not protected when you need it most.