But what makes you so sure that continuity is important? I’ve known people who hit their heads pretty badly and stayed unawaken for several hours. Does that mean that the person that woke up was just a clone? If you mean physical continuity (the same atoms being part of your body), they are constantly replaced during your life anyway, so the atoms in the body of the 10 years old you are not the same as the ones in the 50 years old you. I don’t see why continuity need to be so important, and if it is, then we shouldn’t be worried about death more than we are about temporarily losing consciousness or having the molecules in our body naturally replaced as time goes on. How do we keep personal identity without continuity? I have no idea. That’s one of the big questions in philosophy, but I see no reason to be so attached to the idea that continuity itself is important.
To be fair, I’m not saying I don’t have that weird intuition that continuity is essential as well, but science has shown us many times that our intuitions are often wrong, and when I think rationally about the matter and see all the weird situations that would cause, I’m very inclined to think that that is just an intuitive (and wrong) notion I have, not the most likely actual answer to the problem.