I'd say it's fundamental, and on the short-term, we all understand that as a civilization. That's why every society protects its member from threats, including crime, fire, natural disasters, famine, war. It's not just about quality - you may live the happiest of lives, up until the point a bullet enters your brain[0].
I think there are three main moral reasons for fighting death:
- suffering in the process of death itself
- existential suffering of knowing your time is limited, and that of knowing you're about to die
- suffering of those who you leave behind
Efforts against #1 connect to quality of life, and with progress on that field, it could be resolved. #2 and #3 won't go away until we achieve (effective) immortality, and for many (myself included) they are the reason to support life extension. But maybe you're right, that a stronger pitch along #1 would help gather extra support.
Then there are economic debates about whether our societies could survive sudden doubling of expected lifespans, or whether we'll be able to offload people fast enough to off-world colonies. I say, we'll figure it out as we go along - it's a nice problem to have, as opposed to death.
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[0] - probably one of the most humane ways to die; one can hardly leave this world without suffering during the process of departure.