My argument against quantum immortality, assuming the pop science version of many-worlds interpretation does hold, is as follows:
It's possible to observe yourself in a universe where you'll certainly die. When a person is decapitated, or a person's heart is destroyed (think: heart ripped out of your body Mortal Kombat-style), consciousness does persist for a few seconds. In those situations, you're in a position of essentially certain death while remaining some level of consciousness. Any parallel universe version of yourself that survives cannot be identical to one where you're already experienced decapitation and know you're dead, thus they can be treated as separate beings/consciousnesses. If there is a universe where you could be revived, it's not this one.
Therefore, I believe that you can die even if the pop science version of many worlds ("there is a universe for every possible action we do") is true. Once you die, your consciousness is either terminated or "goes somewhere else". The latter option might be scary, but who knows where and when? You could be revived a century later, or simulated in the future millions of years later. You could have your consciousness transferred to another person from any time/location/universe. Your brain could be reconstructed in the boundless years after the heat death of this universe. Or you could end up in any possible depiction of the afterlife, since none of this is falsifiable. For all you know, in your new body you'll find existence worth suffering for.
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For uncertain means of death, like getting shot or dying of disease at old age, it's trickier. But A. you can die despite "needing" to witness yourself dying, and B. either it's possible for your consciousness to be terminated for good, or for consciousness to be transferred elsewhere after death (where the end result is completely unknown). So I believe it's possible to end our current existence as we know it, which is enough for me.