Now tell me, why would someone want to do this?
Some people are starting to gnash teeth and send up loud cries about this, but I'm genuinely confused. The 22nd Amendment is a relatively new one, and the republic stood just fine without it previously. I'm guessing there are at least two sides to the argument.
On the one hand, you have those who would argue that we did fine pre-22nd, we would be fine without it. That is a distinct possibility, but I find it to be thin and unsupportable.
The other side can argue that the rise of mass media, the speed of communications, social media and the 'cult' aspect of the modern presidency mean the 22nd Amendment is a vital check on all of the above. Let's face it - each day our republic turns more and more into a democracy. To put a fine edge on it, replace 'democracy' with 'mobocracy'.
The power of unthinking, cowed, obsequious masses was not an unknown in 1787, and for that reason, among others, our government was established as a representative republic with democratic principles. After all, you can technically have a representative republic based on authoritarian principles (see also: Communism). So if the founders so feared the mob, why did they not institute term limits in 1787?
The answer to that is very simple and relates to their 18th century outlook on people and government. The theory (proved wrong, now) was that men (and eventually women) without merit or virtue, without courage or conviction, would summarily be voted out of office, replaced by some better representative or executive. In other words, an informed public simply would not tolerate Criminal Congressmen or Presidents. On the other hand, if a leader was effective, meritorious and upstanding, the people should be allowed to retain that individual. Good leadership is good (in the absolute sense of 'good'). Naive? Perhaps. Unreasonably so? Not for 1787.
And the founders instituted other safeguards, among them the electoral college. Yes, another thing the ignorant masses want to see abolished, which would take us even closer to a democracy. The picking of electors, and the fact that electors are constitutionally not bound to vote for any given candidate, meant that enlightened electors could see a fraud for what it was and say "No" to the fraud and put in place someone worthy of the presidency. It is counter-majoritarian, and that is precisely why parts of our system worked so well in the past. If something contra to the majority gives you the willies, stop and follow along.
What is another government institution, partly legislative, partly constitutional, in origin, that is counter-majoritarian? The courts. One man or woman in a black robe, perhaps a collection of 9-15 men and women, and in some cases final say on "what the law is." Why is this notable? Over two centuries of counter-majoritarian institutions have given us things like Heller, McDonald, Brown, Marbury, and plenty of other notable cases that have fundamentally altered our relationship with the Constitution. We could pick apart all those decisions until doomsday, but the fact remains that we put our trust and faith in the courts to come to neutral and correct decisions on critical matters of law and governance.
Back to the 22nd Amendment, you can see that we are a nation where the majority-mob is explicitly to NOT be trusted. We are expected, if not required, to install good, smart people to do a tough, ugly job. This mistrust of the majority is part of our Constitutional DNA, if you will. Unfortunately, I think that today our government is controlled by the majority mob, and representatives are immoral, unethical, lack virtue and courage and simply will not go against a mob for one simple reason - the desire to hold elected office. This is not the system brave men (and women!) risked their lives for 230 odd years ago. This is the system they hoped to avert. Their best plans did not work, unfortunately, and so we are left with either 1) band-aids or 2) wholesale replacement. Band-aids, as those of you with children probably know, eventually fall off or never work well to begin with.
It's time to pay full freight and do what needs to be done, starting by removing each and every corrupt politician, at every level, with your votes.