Two-term limits were set via an Amendment, I believe. It is not as 'concrete' as Articles in the constitution, which had no time-limits, orignially. Still, amendments carry weight.

Congress approved the Twenty-second Amendment on March 21, 1947, and submitted it to the state legislatures for ratification. That process was completed on February 27, 1951, when the requisite 36 of the 48 states had ratified the amendment (neither Alaska nor Hawaii had yet been admitted as a state), and its provisions came into force on that date. The amendment prohibits anyone who has been elected president twice from being elected to office again. https://en.wikipedia.org/wiki/Twenty-second_Amendment_to_the_United_States_Constitution

This was done because Franklin Roosevelt had four terms, and the last years he was basically like Biden, in terms of health. But hey, there was a war on. The lesson learned was: being a president is a hard, and stressful job, all in the public eye. The difference between Roosevelt and Biden was that we had millions of cameras, this time around. The congress in 1947 decided to set boundaries, and allow two terms only - given the example of Washington, who refused a third term, due to feeble health. (Don't mention the war conducted by wifely pen, we think we managed to make it look legit, honest)

I like to compare this precedent with another superpower, but with a man who is healthy: Putin started fairly young (but well qualified, and work-exposed): he did two terms, had Medvedev take a term, and now he is doing a second round of two terms. Of course, Russians actually like that - not only because he is eminently competent, but it also provides stability, and the economy, and all sorts of things, are only impoving - so why vote for someone untested? The Russian people voted for Putin every time, and he only gets more popular.

The argument is: It takes more than eight years to build trust, even when just moving into a new town - here in New Zealand it is a running joke amongst furreners like me, that it takes 15 years before people recognize you and wave out to you, and even then they'll need to see you once a week at the same time, walking.

To compare: in England, it takes about ten years to 'become' a local, but someone will happily strike up a conversation, especiallty in the pub. In New Zealand it is like people are really surprised if you even look at them funny.

In the USA, everyone is something. My favorite quote on that subject is

"the most remarkable man in the country",

which I have found applied to just about every person I met. Excepting one blue-collar stranger in a fraying jalopy, who helped me once - never saw him again. The quote is used to describe Mr. Pecksniff, a character in "the Chuzzlewits", by Charles Dickens. The main character travels to the East Coast USA during an election season, and witnesses the spectacle. Mr Pecksniff (note the nasal reference) was known for his hypocrisy and self-serving nature.

So it boils down to choice. Do the people want a competent, popular, well-tested president to have more than two terms? The congress in 1947 said: never again will we subject the American people to a senile-man-in-a-wheelchair, with a wife-ly signature. They decided to pass 22A FOR the people (did the people vote? I guess so). But in a way, the exercise was a cover-up, because those in Washington, sniffing the swamp-vapors, so to speak, KNEW that Rosie-baby was a basket-case. And they remained quiet all that time.

Oh wait. Even one term can suffer that fate ...

Maybe the two-term fix (i.e. 22 Amendment), does not prevent dementia and autopens. Why is 22A even there, if it does not work?

Also Slightly OT. But you see, Obama cannot run again, because of the 22A