I'm assuming this is not intended behaviour based on the fact that other scoreboard statistics of  the same type (sprint_one_cm, sneak_one_cm, etc) work differently. Basically, the statistic 'fall_one_cm' only updates when you touch the floor, or stop falling. One would expect it to function like other statistics, that update values constantly while moving.

To reproduce, simply start a new world in creative mode, with cheats on.

Enter the following:

/scoreboard objectives add fall minecraft.custom:minecraft.fall_one_cm
/scoreboard objectives setdisplay sidebar fall

Now find a large height to fall from (that won't completely kill you) and enter survival mode.

Jump, and look to the right for the value to appear. It will only appear once you have hit the ground.