Why aren't there upper-age limits for serving on the Supreme Court or as the President of the United States?
What if while in office one of these officials starts to develop dementia or some other age related disease that affects their judgement or thinking skills?
The short answer is that no one thought to include such provisions in the United States Constitution that was adopted in 1789, and that it is very hard to amend the United States Constitution (although one amendment that partially addresses this concern, the 25th, has been adopted).
This is understandable. Dementia at an advanced age was a significantly less salient issue in 1789, when life expectancies were much shorter, than they are today. The average life expectancy in the time period from 1750 to 1800 was 36 years. Even conditional upon attaining age 20, the life expectancy for white men was under 50 years of age, throughout the 1800s. Most people died before they were old enough for age related dementia to be a major concern.
The upper age limit for serving as U.S. President is eight years older than the candidate was when he was elected, with voter review after four years. If the voters elect someone, they do so with the understanding that the President will serve at least another four years and evaluate for themselves if that is too old. In practice, age is frequently raised as an issue in the Presidential nomination process and in Presidential elections, although it is hard to identify a particular election in which it was a decisive factor.
The same thing happens in every legislative election.
Also, the 25th Amendment to the United States Constitution was adopted to address the question of Presidential incapacity, and federal legislators can be removed by the house in which they were elected for cause by a two-thirds majority (U.S. Constitution, Article I, Section 5, Clause 2).
In the case of judges, there is only the remedy of impeachment for non-feasance resulting from failure to carry out the duties of the office as a consequence of old age related conditions. But, the compensation system for federal judges in the United States creates a very powerful economic incentive to retire at a reasonable retirement age by virtue of how the defined benefit pension plan works, that most judges assent to not long after reaching that age. As explained in the linked material:
Financial concerns were paramount for judges who retired after senior status, as well as for judges who retired directly from active service, according to the survey results presented on Sunday. “I wanted more income” was the most popular reason cited for retirement for both groups. . . .
Federal judges can retire or take senior status, with the option of a reduced workload, if they satisfy the “rule of 80.” The requirement says they must be age 65 or older, and their combined age and years of experience must total 80. It is an attractive option because their pay remains the same, but their taxes fall because they don’t have to pay taxes for Social Security or Medicare.
In other words, if judges retire once meeting the "rule of 80" they can get the same pay with less taxes without doing any work, and can take senior judge assignments in the discretion of the chief judge of their court for additional pay, while vacating their position. If a chief judge feels that a senior judge is no longer intellectually able to do the work, the chief judge can decline to assign a senior judge to more cases.
Only at the U.S. Supreme Court level is the power associated with holding the post so great relative to financial considerations, that the compensation system incentives don't work, and it is arguable that in the case, for example, of Justice O'Connor, that the compensation factor was an important reason for her resignation.
The concern is also mitigated at the U.S. Supreme Court level, and even at the Court of Appeals level, because those judges mostly make decisions as part of a panel of judges, rather than individually. So, if the other judges on the panel make the right decision, the incompetent judge's decision doesn't matter.
For trial court judges, the prospect of appellate review of their decisions partially mitigates the risk of a judge making bad decisions due to declining intellectual capacity.
Most states have chosen not to follow the federal example with regard to judges and have either imposed a constitutional retirement age, as in the case of Colorado, where Colorado Constitution, Article IV, Section 23(1) requires judges to retire at age 72, and/or have a commission overseeing judges (and sometimes other civil servants) that can require them to retire due to disabilities which often arise from old age.
Term limits, which are common at the state and local government level, also often impose de facto age limits, because most very elderly elected officials mandated to be so old by being re-elected many times after being first elected at a much younger age. Term limits limit the extent to which this can happen.
The short, cynical answer would be that laws have mostly been made by old men. Further, that older people tend to look at younger people (not without some justification) as less "wise", experienced, and competent, and that older people too frequently do not imagine or perceive their own decline in ability, and even if they do they have no interest in giving up what power and privilege they may have acquired.
If you made the laws, in any country, under any form of government, would you make one that forced you to give up anything? Why would it even occur to you to do such a thing?
Excluding people based on a personal attribute that is not under their control due to some statistical correlation is pretty much the textbook definition of discrimination. Discrimination based on age is sometimes also called ageism.
In most modern Western societies – including the United States – most people strongly believe we should judge people based on individual merits. This is a position help by both the left and right, although opinions differ on how to best enact on this (e.g. see affirmative action).
This can be traced back to (classical) liberalism and individualism, which has massively influenced almost all modern Western political views.
In the specific case of age-correlated mentally debilitating diseases, some people develop Alzheimer's disease as early as their fifties – known as early-onset Alzheimer's disease – while other live to be over a hundred and never develop it.
It's true that age is correlated with an increased risk of Alzheimer's disease and other causes of dementia, but it's far from a certainty; it only develops in about 5 to 8 per cent of people. In other words: it's far from certain that Alzheimer's of some other disease causing dementia develops.
The obvious question is, what would the age limit be? If you institute any age limit it would almost certainly be accused of being Ageism.
Your main question, what would happen if someone gets something like dementia in office, is largely covered by section 4 of the 25th amendment (emphasis mine):
Whenever the Vice President and a majority of either the principal officers of the executive departments or of such other body as Congress may by law provide, transmit to the President pro tempore of the Senate and the Speaker of the House of Representatives their written declaration that the President is unable to discharge the powers and duties of his office, the Vice President shall immediately assume the powers and duties of the office as Acting President.
So in other words, if the VP and enough members of government agree that the president is unable to discharge the duties of office for any reason (such as dementia) they can remove the president from office immediately.
