Alzheimer's treatment levels the playing field by restoring to sufferers something of which they have been bereaved: normal mental function. Even if only a subset of the population has access to it, all they're gaining is normalcy. Moreover, it can plausibly be comped by health insurance, especially in countries with universal healthcare. In a healthy economy, the political class has an incentive to keep workers healthy and productive longer, and to reward them for their service with a comfortable and dignified retirement, by making such medicines available to them.
Conversely, pure life extension creates an exceptional state of existence—no one except those using them has a chance of living a thousand years. The wealthy have a clear-cut motivation not to let these drugs become readily accessible, as it is a competitive advantage that feeds directly into their pecuniary pursuits; they no longer need to worry about:
1. Dynastic management (heirs are unreliable—be your own);
2. Estate taxes (the government wants some of your money—hiding it adequately can be tiresome);
3. Religious threats of punishment after death (if such things matter to them—probably not); or
4. "You can't take it with you," which is perhaps the main reason why billionaire philanthropists exist.
As such, we aren't going to see lobbying efforts to democratize life extension cures—ever. There are real incentives for the rich and powerful to lobby against such a possibility.
Finally, we already know that many proponents of life extension research in the VC space have neo-reactionary sympathies or aspirations; our favorite whipping boy Peter Thiel has contributed directly to the "Dark Enlightenment" movement. These are people who are not hiding their desires to become feudal lords and absolute despots, and not taking them at their word in such matters is the sort of 5D mental gymnastics that belongs on 4chan.
It is much less of a problem if the playing field is level, which is an eventual outcome with conventional quality-of-life efforts like Alzheimer's research. While it is not out of the realm of science fiction possibility that all humanity could someday be blessed with the gift of immortality—as well as fix the planet and somehow keep our population at a replacement level—the nutjobs currently militating for it are about as trustworthy as a Ferengi handshake.