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Presidential term limits and the fact that it has been tradition where many President step down from most major politics after their presidency. With a few exceptions of course
For retired presidents they usually feel they can use their platform to focus on projects that are important to them, and only dip back into the world stage if they feel they can bring weight or influence to something. Carter and Clinton have both negotiated prisoner releases with North Korea, for example. Former presidents have also been influential in raising funds for humanitarian relief (Clinton and Bush Sr worked together after the tsunami in 2004). Also don’t forget that ex-presidents can make an absolute fortune for speaking engagements, and also on book deals. But really, for most people that serve as president, that was the culmination of a lifelong goal. They are ready to move on to something else. Eisenhower painted and golfed. Teddy Roosevelt hunted and wrote books. Jimmy Carter is a Sunday school teacher and builds houses.
Other statesmen do occasionally get back into politics, and John Kerry is currently the special envoy on climate. After Mitt Romney lost his presidential election bid in 2012 he moved to Utah and was elected to the Senate and is still there. 
There is precedence (though it was a long time ago) for former presidents to keep serving in other offices as you suggested. John Quincy Adams was elected to the House of Representatives after he left the presidency. William Howard Taft was appointed Chief Justice of the Supreme Court, and by most accounts he was much better suited to that role than the presidency. >

Teddy Roosevelt ran against his successor (the candidate he earlier had supported/promoted). He is an exception to the rule, though. >

And after he lost that campaign he went to South America and almost died mapping a river in the Amazon. His entire life was an exception to the rule. >

Teddy Roosevelt was an absolute badass. >

Then proceeded to speak for something like an hour and a half. He’s basically the Chuck Norris of US politics. >

Considering Chuck Norris was an actor who only played someone tough on screen, I'd say Ronald Reagan is the Chuck Norris of US politics. >

He was world karate champion, so a bit more than acting tough >

I think an overlooked factor not mentioned yet is they are tired.
For the last 4 to 8 years you lived with the knowledge that there was always a chance you'd get woken up at 2 am, or pulled out of lunch, or whatever and told that the military had detected what it thinks is an incoming Russian full scale nuclear strike, and you have 3 minutes to decide if you want to kill 100 million people in response to this suspicion. 
Like what the fuck. Sure. I can type those words. But the situation is so insane I'm not going to pretend to understand the emotions and stress that must come out of being actually in that position where that phone call might come to me. 
And that's just 1 tiny part of a president's life. You then take into consideration that they are basically working a shift for 4 to 8 year straight. You never really are off work when you're the president. The decisions you make daily are life and death. The "lesser" decisions you make might create a million poor people instead of lifting a million out of poverty.
The meme of the presidents aging 10 years in a 4 year term is a meme for a reason. 
If I had just gone through that, I'd want to be done working. I'd have literally 0 interest in going back on the campaign trail to get a job in the house of representatives. Those 4 to 8 years were more than enough given to my country. I'll take whatever left in my life back for myself. >

To add to it, I think those of us old enough to have lived through a few presidencies recognize that there is in fact a continuum of world events that span multiple presidencies. The president (or any elected and termed-out leader) is just one cog in history. They run the machine for a bit, and then another comes along. Expecting someone to come back and “fix things” is antithetical to the system, and I bet if anyone understands that to their core, it’s the person who sat in power for their term. 
I get the sense from former presidents (Trump excluded) that they understand that the person coming in behind them is a successor, and they need to support that, and get out of the way. >

Why would they want to? That's like retiring from CEO and coming back as middle management. >

I’ve actually known some senior level engineers that love nothing more than coming down to the lab and running through test cards with the technicians. When you’re at the top you lose a lot of the joy that comes from the basics. I’ll bet personal job satisfaction is much higher with small town mayors than with presidents. >

My buddy is in the USAF and has had multiple high ranking brass from his deployments offer their letters of recommendation for him to become an officer instead of enlisted. This is his exact reason, he likes being with his airmen/women. He knows once he ends up as an officer that is going to be a mostly deskjob. >

Most people who become president do so late in late in life around mid 50s or later and after service are normally 60+ and economically independent >

Because they all make way more for private speaking fees than they ever did in public service. >

Former POTUS' bow out and leave things to the rest of us, seeing as it's no longer kosher for them to be wielding that highest power of the land, either vs. a sitting POTUS or over all the rest of us. Jimmy Carter's post Presidential service has been exemplary of a Man of Leadership since his leaving office. Mr. Obama and even more importantly, Mrs. Obama's service to the world has also been exemplary, with neither taking anything from successive Presidents yet not ceasing to provide leadership. >

As far as former 2 term Presidents go, it's the same reason Elon Musk won't go to work at McD flipping burgers. >

Kerry is still in politics. He is the US Special Envoy for Climate. Moreover, he remained as a Senator after his defeat in 2004, and served as Secretary of State in the Obama administration. >

I think you’re specifically referring to elected political office as opposed to just “politics”. They are all deeply involved in politics whether they make it publicly obvious or not. Obama publicly returns for general campaigns and helps shape things behind the scenes otherwise (as do the others best they can). Biden ran for President 3 times, Hilary Clinton twice and recently tried getting back into the game with limited appetite for her return. They are all still deeply involved with the donors as well that shape the general landscape of their parties. Even Jeb with the stink of failure on him from his lackluster run in 2016 is still involved with party politics, fundraising, etc. >

Usually former presidents are valuable advisors for their successors. This has certainly been true of Carter, Clinton, Bush sr, Bush jr, and Obama.
Clinton was known to have consulted former President Nixon on foreign policy.
W has been more valuable as a former president than he was as a president 😄
However, some former presidents have served in government after leaving office. President Taft was appointed to serve on the Supreme Court, to give one example. >

Great American writer Mark Twain once said, "Politicians are like diapers, they must be changed regularly and for the same reasons." and I think he had the right idea. Once politicians get into the sausage-making of actually holding office, it's almost impossible to avoid building a record that will be at odds with the expectations had of them when they were candidates. Look at how Alexandria Ocasio-Cortez is already receiving a lot of criticism from anti-war progressives for voting in favor of funding Ukraine, or for her votes to fund police. Give her another 20 years in the House and she'll have enough of a record for just about anyone to criticize her about anything.
EDIT: Also, Hillary Clinton herself had a solid "return to politics" after her time as First Lady with her time as Senator and Secretary of State. >

Being president and even being a presidential candidate is agonizing AF. I would assume, as someone said, that they are tired after that grueling journey ESPECIALLY if they’ve been the president. With that said, as it was stated somewhere else, a lot of them are not viewed the same now as they were in their time because a lot has changed. More people are aware of their flaws, so they may not be viewed positively in the present no matter how their presidency/campaigning went. >

Thanks for the answer