A bit of raw data to feed the debate.
FCTM for long range aircraft states : "if the flare is initiated too low (below 25ft), then the pitch changes will not have sufficient time to allow the necessary change to aircraft trajectory. Late, weak or relased flare inputs increase the risk of a hard landing" (I just checked it for one airline)
FCTOM for single aisle aircraft has the same line only without the 25ft value (also checked it for just one airline)
I've seen cases in which a full back stick input from 20ft down to the ground was not enough to avoid a hard landing (for SA aircraft).