I don't know about that. People buy fuel scoops so they won't end up stranded in the middle of nowhere, and if you prevent fuel scooping off white dwarfs, people might end up that way if they find themselves in a white dwarf system without any gas giants.
If the devs want to make a point of this, I'd suggest that the fuel scoop would be able to scoop up trace amounts of hydrogen. After doing this at supercruise speeds, the player would be able to gather just enough hydrogen to make another jump to scoop a main-sequence star.
I believe that the primary fuel used in Elite is hydrogen. White dwarfs have burned off most of their hydrogen and so are not ideal for fuel scooping, I am thinking. Perhaps you could be allowed to scoop at a MUCH reduced rate to reflect the low amount of hydrogen available. I like the idea of scooping trace amounts of hydrogen while in supercruise! I would also imagine that not all gas giants would useful for scooping fuel as I am sure many of them don't have abundant hydrogen.