(1) A country can only have one ruler, and Americans in particular expect Presidents to leave office and age gracefully. They don't want them staying in politics. Violate this rule at your peril.
(2) In fact, only two violated this to a degree in recent history. Jimmy Carter took shots from the sidelines and tried to interfere with foreign policy. He was basically ignored or treated as a joke. Bill Clinton took forays into politics to help his wife, and tarnished the hell out of his image. He was smeared as a racist in 2008 and he was smeared as a fool by his wife's campaign in 2008 and 2012. Now he's gone from "two-time winner" to "hurdle that helped his wife become a two-time loser." Obama seems much more likely to fall into the Clinton example. Why? Read on...
(3) Bill Clinton was never a great politician. He won the White House in plurality votes (never coming near 50%) because H. Ross Perot was determined to destroy Bush and then thought he might win against an unpopular Clinton and the terrible Bob Dole. Clinton did win, true, but he also managed to end a near Century of Democratic control over the House and only slightly less control over the Senate. He lost the South finally for the Democrats and he failed to keep the Democrats from drifting into the land of Identity Politics, which have doomed them now (that was actually his goal coming to power). In short, winning was the only thing he did right and he only did that because other people beat his opponents.
Nevertheless, Clinton was celebrated by the MSM-left as a genius because the left wanted him to be a genius. His friends in Hollywood made movies about him and gave him celebrity status everywhere. The MSM hired away all of his staffers and filled their ranks with his supporters, who then talked about his communication genius and his brilliant ability to reach the public. In other words, they invented a myth. Suddenly, his two victories were triumphs rather than squeakers. In fact, consider this. The genius, at the height of his popularity, couldn't help Al Gore beat an unqualified ex-drunken moron. His failure was excused as being about a stolen election and wooden candidate, but Bill failed to deliver. Then 2008 and 2012 exposed just how bad a politician he really was. Not only could he not reach a skeptical public, but his own supporters were embarrassed by him.
The media had a crush on Obama. He was the perfect black man of their dreams... "clean", progressive but sounded like he could appeal to middle America, "no negro dialect", educated, OMG's he's amazing! Consequently, they decided he was an amazing candidate too. Then he beat the mental-case version of Yosemite Sam and Reality-Trash Palin, and the left knew he was genius! In fact, he's the greatest politician of all time! He even won re-election against the Mitt 'Bologna Sandwich' Romney to prove it. He's dreamy! makes googly eyes and sighs wistfully
Um no. Obama relied on his opponents falling apart and offered one selling point: "I will tell black America to stop being a bunch of race-obsessed whiners." That's it. Oh, and he read well from the teleprompter. He lacked Clinton's ability to reach normal voters. He lacked Clinton's ear for the issues that mattered. He lacked Clinton's desire to do something worthwhile.
All of this became increasingly obvious as his failures piled up. He did nothing to build a consensus that would let him lead. He couldn't even build a consensus with his own party. He failed to support the Democrats and took them from the point of absolute power in the US to their worst position since the start of the 1900's. He was never able to work with any foreign leaders, to sway the public on any issue, to identify issues that mattered, to control the public agenda, to pass laws, to pass regulations, or to put his ideas into play in any way. He lost millions of votes in his re-election bid (something that's never happened before). He wasn't even able to help make his own voters turn out to either keep Hillary from winning the primaries or help her win the general election.
Like "Bill Clinton, Brilliant Politician and Most Popular Man Ever," Obama as a brilliant politician is a myth. Objectively, the man is a total failure, whose only skill was that the GOP ran two awful candidates against him. Getting back into politics will only prove this as Obama lacks the wit, drive and interest in politics to deal with Trump, who will not bend over and let Obama kick him. Moreover...
(4) Obama will be shocked by how little support he will have. The most fundamental problem Obama faces is that he will stand in the way of the other Democrats. Right now, the Democrats are in a civil war to decide how to re-allign themselves in a post Obama world. Who will lead them, who will control the voice and wallet of the party, etc. Obama sticking his nose back in will crowd out those who are fighting for these spots. He will not be welcome. And since he brings nothing to the table except memories of an unpopular presidency, look for this to go wrong fast.
So hey, bring him on! Unfortunately, if Obama has proven one thing over time, it is that he is lazy. I don't see him bothering.