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A VOLUNTARY EUGENICS SCHEME
In 2020, caring for people with Alzheimer's will cost an estimated $305 billion. This is just the cost in the US alone. This also seems like a notoriously hard disease to find a cure against. An estimated 5.5 million people in the US currently suffer from Alzheimer's, most of whom are over 65. Even if thrice that number (~16 million) are young carriers of Alzheimer's, we can solve this more effectively.
If the government introduced a contract which awarded $30000 to people who were carriers of Alzheimer's on the condition that they do not produce children, we will manage to significantly reduce the number of cases. These people can still adopt children, those who will never suffer from Alzheimer's. Think of the generations and generations whose lives will become so much better. Moreover, this whole scheme is voluntary. Nobody has to be forced into compliance, they can adopt children instead of reproducing and get $30000 wired to their account. There are several demerits of this approach:
1. Less than 1% of that amount, roughly $3 billion is also spent on Alzheimer's research will also help us understand other neurological diseases better. If all that money is given away, we will also give away the chance to understand the brain better.
2. A scheme like this will be very hard to implement and is easy to game. I could take the $30000, have kids and then make them take $30000 again and so on.
In order for a voluntary eugenics scheme to work, the trait must be genetically heritable. What evidence is there that Alzheimer's is strongly genetically heritable? If there was a gene for Alzheimers, we could perform genetic testing and then implement the scheme you described. Personally, I'm pretty skeptical that this is a good use of money, for a few reasons.
As you said, the majority of suffers of Alzheimers are over 65. That means that it will take a minimum of 65 years for this scheme to start having any big effects. Over such timelines, I think it's plausible that there are more powerful technologies on the horizon. For instance, rather than focus on old-fashioned Eugenics, why not push for genetic engineering as a solution to Alzheimers?
You're absolutely right, Alzheimer's is a bad example. My intention was to show that an alternative strategy of this kind may exist for 'curing' certain diseases.