But he should. Not because it would be the best thing for the country. He doesn't care about this country or its citizens (except for a few family members and some rich friends). But because it would be in his own best interest.
Trump is in some serious legal trouble. I'm not talking about his Russia problems (although that could still bounce back on him), but his more recent actions -- things he has done after losing the election to Joe Biden. Specifically, trying to pressure election officials and legislatures into overturning the will of the voters, and urging his supporters to attack the Capitol to force lawmakers into keeping him in power (promoting a coup).
These are serious charges, and unless he is given a pardon, could result in years in a federal prison.
It is reported that he is considering many pardons for his family and aides to be announced a day or two before leaving office -- and that one of those pardons would be for himself. That's not going to work.
A self-pardon would be immediately challenged in Court, and likely be voided. Allowing a president to pardon himself would mean he was above the law. No one is above the law in this country. While the president is powerful, and cannot be arrested or charged with a crime while in office (according to a ridiculous Department of Justice ruling), it would be unconstitutional to allow him to be above the law after leaving office.
A self-pardon could also bounce back on him. By pardoning himself, he would be admitting that he thinks he has broken one or more laws -- and that could be used against him at a trial.
He does need a pardon, but there's only one way to get one that wouldn't be overturned by the Supreme Court. He would have to resign, and hope Pence would give him one (like Ford pardoned Nixon). Of course this would mean mending his fences with Pence -- after condemning him for not breaking the law to keep Trump in power, and urging a mob of supporters to go after Pence.
He brought Pence to the White House on Monday, and aides said the two men had a pleasant talk. This makes me think he is trying to get back in good with Pence -- in case he needs him for a pardon.
Will Trump resign? Would Pence pardon him if he did? I don't know, but it is the only path Trump has to get what he needs -- a pardon. We'll have to wait and see if he has enough sense to realize that.