You're right, Lincoln and Roosevelt have two terrible, glaring and shameful mistakes in their presidency. But Lincoln also preserved the Union, prevented secession and began the process to the true end of slavery. FDR helped curb the Great Depression and if not end it, give Americans confidence and hope in capitalism again when all of that was dead in 1932 and prepared America for its finest hour and led us through the most harrowing test our country faced in the 20th century, WWII, with amazing aptitude and success (the war effort was, as you know, what pulled us out of the depression).
Nixon's entire presidency really circles around Vietnam and Watergate in the history books. He promised peace in 1968, could have given it to America in 1969, but chose to wait three years while thousands of Americans died and started a secret war in Camobdia, thinking a civil war that left millions dead would help the American cause.
Opening China and streamlining social security does not make up for that fact. And Nixon committing a felony, or as he says "When the president does it, it is not a crime," was just the final nail in the coffin. I admit he is not as bad as some people act in satirical fiction or the immense hatred for him in the '70s believed, but he was still a president who failed his social contract with America and defamed the office so much, Americans have never trusted a president again without a large degree of cynicism and disdain.
It still boggles my mind to think how one could rationalize this man to be in the same list of FDR and Lincoln. Or Washington, Teddy, Truman, etc.