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.