Even though neurological testing would help to exclude from presidency those with cognitive impairment, such as from early Alzheimer’s disease, Parkinson’s disease, and other causes, it does not offer much help in diagnosing a patient who refuses to recognize his / her current condition. (And I think most of us would agree there are all kind of issues if we were to try to expand this testing to predict future diseases and the impact it will have on an individual.)
President Biden's situation, unfortunately is quite common, in that the vast majority of persons with cognitive decline or serious personality disorder are unaware that they even have a problem. This is usually not due to active denial of pathology, but rather due to a phenomenon called "lack of insight" or what neurologists call "anosognosia".