I don't know why this is, but dementia is often a continuum, and the decision making that people make seems to change in early dementia.
Unless you are proposing that others get to make this executive decision that people with dementias lives aren't worth living, this solution is not practical.
More practical would be to accept that we are far better off over-medicating with pain meds to "keep people comfortable" with the implicit idea that it will shorten their lives. Everyone can pretend we're doing it for pain. Effectively it's like what you said but with some face-saving bullshit where no-one has to admit we're killing grandpa/grandma over the course of a few months. I'd much rather a few months on opiates at the end of my life than a few years on Haldol (JFC). Ugh.
Is it really demented thinking to want to avoid approaching death? I am there right now with my mom, and if she wants to press on, who am I to argue?
On Monday I will be an Intel Principal engineer again - but there's some Monday where I may need someone else's help to get the shit off my bum. From the perspective of that next Monday the indignity of the latter one is astonishing and humiliating, but there will be many intermediate stages where I get used to the idea that I am not what I was and to see that life is still quite pleasant.
If it's reasonably certain that I will die soon or there is no chance for recovery I would like to try all kinds of drugs like heroin, cocaine and others. Why stay sober?
More likely it is that theoretical death sometime in the future is something much different then real death sometime soon. Which is much different to actually doing it and following up.
The exact same thing happens in physical danger situations. People are brave and daring and when faced with actual situation, the start making real decision differently.
Personally I think I would prefer euthanasia if I knew I was developing dementia and likely to end up in a care home similar to the one described in the article, or even one much better than that, so perhaps selfishly I would prefer a society where such is legal even though there would end up being abuses like you describe.
We can think of care homes as like suppliers in a captive market, and we are the consumers - but it is even worse that a captive market in the sense that at least in a captive market you have the option not to buy, whereas we will be forced to. The existence of assisted dying as an option may even economically incentivize the care industry to improve.
If they are fabricating schizophrenia dx, then they would also likely to fabricate medical cause for euthanasia.