FDR was quite explicit that he would not run for another term once peace was restored:
"I have already indicated to you why I accept the nomination that you have offered me — in spite of my desire to retire to the quiet of private life.
You in this Convention are aware of what I have sought to gain for the Nation, and you have asked me to continue.
It seems wholly likely that within the next four years our armed forces, and those of our allies, will have gained a complete victory over Germany and Japan, sooner or later, and that the world once more will be at peace — under a system, we hope that will prevent a new world war. In any event, whenever that time comes, new hands will then have full opportunity to realize the ideals which we seek."
https://archive.org/stream/4926605.1944.001.umich.edu/4926605.1944.001.umich.edu_djvu.txt
Now, yes, of course sometimes politicians break promises not to run again. But to add a fifth term *in peacetime* after you promised not to do so is going to cost FDR some votes. How many I don't know, but it is going to have an effect. There are going to be *some* voters who gave FDR the benefit of the doubt in wartime but who will now say "Maybe the Republicans are right about his 'Caesarism.'"