If Alzheimer was simply a deficiency of nutrients, I wouldn't think this way, but if it really is a protein that "can be cleared", why did it get there in the first place?
Your core question is a good one and fundamentally raises the question of causality (which came first, the A-beta or Alzheimer's disease, AD? See ref. 1 for a 'simple' discussion).
Interesting evidence comes from people with genetic mutations that decrease the levels of the precursor to A-beta (the protein associated with Alzheimer's plaques). People with these mutations are less likely to develop AD, suggesting that A-beta is related to the root cause of AD. The OP supports this evidence, as removing A-beta plaques ameliorates some memory loss.
As a final, unrelated note, I don't know much dermatology but I haven't gotten the sense that our response to uroshiol is considered protective. Unlike A-beta, uroshiol is directly causative of its associated clinical symptoms[3].
1. http://www.mayoclinic.org/diseases-conditions/alzheimers-dis... 2. http://www.ncbi.nlm.nih.gov/pubmed/22801501 3. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC294319/
What could possibly be worse? What are we seeing from non-Alzheimer sufferers that's so terrible? I don't think there's any evidence here that there's some benefit to it. Its a horrible disease.
My dad went from occasional forgetfulness to completely falling apart in less than two years. He would get lost routinely, couldn't remember names, had no idea what time or day it was, and developed sundown syndrome where once 6pm hit he completely went mad. He would be angry at nothing and scream at the mirror. He would rant and ramble about his past or strange conspiracy theories. Towards the end, he lived in some weird nightmarish state almost all the time. Sundown syndrome became his norm. He died of cancer before it progressed past that point, but man, this disease is not just losing memories. It pretty much destroys your brain and acute dementia has a link with immune system dysfunction, so it eventually kills you, usually by pneumonia.
I doubt there's any benefit. Evolution isn't this wonderful process. Its a lot of crap thrown at the wall and enjoying the stuff that works and dealing with what doesn't. There's no mastermind or clockmaker here. There are a lot of things that go wrong with human health that has no benefit.
Since dementia is a disease that happens at a late age, there doesn't need to be a reason why it is there. It happens a long time after reproduction, so its effect on evolution is minimal, worse it could even be evolved as a mechanism to curb older specimens in the species.
Average (arithmetic mean) life expectancy was a lot lower because it was heavily skewed by infant mortality. Up until very recently, many more babies died within their first few years of life. We've dramatically improved our ability to produce and distribute food and medicine, which has had a profound effect on infant survivability. But we haven't actually lengthened the average life expectancy of an adult who survives the first few years of childhood by all that much.
Point is, plenty of people have been living into their 70s, 80s, and 90s for as long as we've existed as a species. That said, the prevalance of diseases like Alzheimer's might be a fairly modern aberration, perhaps owing to lifestyle, environmental, and dietary factors.
Correct, though largely (not entirely, but very largely) because the proportion of people living past age ~3 has skyrocketed. Correct for that factor, and our life expectancy is actually lower than it was in, say, mid-Victorian England.
(Note, as well, that I'm referring to life expectancy and not, say, the potential maximum human lifespan).
Also somewhat owing to the recognition of Alzheimer's as a disease state (coincident with amyloid beta plaques) rather than just part of "getting old". The difference between "more prevalent" and "better identified" is difficult to determine.