My guess is that its likely a tradeoff between weight and efficiency. An electric motor capable of turning a prop of the size that would provide the performance desired my be too heavy. I've also read that the larger the edf, the more efficient the blades are. Fan swept area increases exponentially with increase in fan radius.
You're the teach, I won't argue... Oh who am I kidding =), I had to check Wikipedia as I didn't learn the terminology in English:
Quadratic growth, 2 as the exponent, like prop cross section surface area: πr[SUP]2[/SUP]
Cubic growth, 3 as the exponent, like volume of sphere: 4πr[SUP]3[/SUP]/3
Exponential growth, the variable as the exponent, like bacteria growing: a[SUP]r[/SUP]
Sorry if I just argue against the language barrier here. And I don't claim to know the formulas for drag, power, efficiency, prop specs et c related to the surface area of an EDF.