Alzheimer's disease and other forms of dementia are not conditions that present for the first time in the form of pilot incapacitation. They are slow-moving conditions with fairly obvious symptoms that will interfere with day-to-day life long before a concern for flying arises. If a person cannot find his way to the airport, he's unlikely to have his condition discovered on the flight deck.
The requirements for flying are the same at any age. There is no reason to have additional requirements for older pilots. If a given set of requirements suffices at age 25, then it also suffices at age 75. The tests should concentrate purely on verifying that a person can safely fly, not on discriminating between age groups with artificial, additional restrictions that only apply to older pilots.
Do away with medicals? No, that probably wouldn't be a good idea. However, many of the requirements and restrictions that exist now could be safely eased or eliminated without any real impact on safety. Aviation authorities are obsessed with the bogeyman of a pilot who suddenly passes out at the controls, but this type of sudden pilot incapacitation is practically unknown, even though nearly the entire process of medical certification concentrates upon it (to the detriment of many other considerations).
You might say that pilot incapacitation is rare because medicals are so stringent. But in that case, you'll have to explain why driver incapacitation is also extraordinarily rare, even though most automobile drivers scarcely need more than a quick vision test to get a license.
You can also see how rare it is just by walking down a street. When was the last time you were on a busy street or in a crowd and you saw someone suddenly incapacitated, dropping to the ground? It's just as likely on the street as it is on a flight deck. And yet it's so rare that many of us have never seen it at all (I've seen it exactly once in my lifetime). And these people on the street are not being given aviation medicals to weed out the high risks.
In other words, the whole notion of pilot incapacitation, whether it be through some medical condition or simply the result of old age (although old age alone never produces incapacitation), is not very relevant in aviation today. There are far greater dangers to worry about, such as simple pilot fatigue, and they are not addressed by aviation medical exams at all.
Checking a pilot's age is pretty useless. It would be a lot more productive to check how much good-quality sleep he has had prior to arriving at the airport.