Absolutely. I try to think of this at a human level first of all, but the financial implications of 'man's' obsession with constantly prolonging life (for the benefit of the receiver or not) are huge and simply cannot be supported. Especially given, as you point out, the dropping fertility rate that will further contribute to a shift in age demographics with more pensioners to support. And as people live longer (either naturally through medical advances, or artificially through machines) there simply won't be enough in the pot to support social services - so we get to that survival based on wealth (which you could easily argue we already have - but that gap will just widen).
What's the answer when, through medical advances, we all live to 150 (compos mentis or not). Make us work to 120 to keep the pot topped up. Fuck that. I would rather be dead at 80 than work for 100 years.
Now, I am not suggesting we take a Logan's Run approach and vapourise people at a set age. But bodies have a natural shelf life. When that is reached, let it be, and let us slip away in comfort when there is no more quality of life. Keep the population balance at a more sustainable level, and allow people to fully enjoy the finite time we have on this planet whilst accepting it is not forever.
And when we are proper fucked got absolutely no life to look forward to, why is it that can we decide a dog or a cat will have no quality of life, therefore it is better for them if they are 'put out of their misery', but we can't do this for a person - instead we need to keep them going for our own selfish wants. It's just wrong. There is no humanity in that. "I'll make you suffer in pain or in a vegetative state because it would be really sad if you weren't around any more and I' not ready to say goodbye" (slightly over simplifying things, but you get the gist).
Our bodies, our choice.
And I am genuinely sorry if I offend anyone with my belief that we should be allowed to die our own way. I have seen a lot of unnecessary suffering and can see no good in blocking assisted dying.