How does the rest of the century pan out?
FDR is still Cox's running mate in 1920, since that antedates the PoD. FDR is thus not a complete unknown at the time of his death.
One wildcard is Al Smith. FDR and Smith were staunch political allies until FDR shoved aside his predecessor to take the Democratic Nomination for President in 1932. Does Smith still rise to run in 1928? Is he delayed until 1932, where Hoover is undoubtedly defeated?
So Al Smith is potentially impacted. Hoover wins in 1928, whether Smith is the Democrat nominee or not. And he loses in 1932, whether Smith is the Candidate or not. John Nance Garner goes for the Nomination. I wonder if Huey Long, Burton K. Wheeler or Cordell Hull tries. The Democratic Primary was decisively settled in favor of FDR in 1932 pretty much at the start. In this situation, Al Smith might not be in consideration--if he runs in 1928, he's been defeated by Hoover. So a potential dark horse takes the ticket and the Presidency.
FDR's 100 days were a critical time in terms of building a massive federal program to attack the Depression. What these men; Smith, Long, Garner, Wheeler or Hull do will very quickly shift the course of the United States.
So, the PoD butterflies widely and quickly.