I vaguely remember reading somewhere that the ability to use a double bladed required quite a bit of concentration. Concentration that those most in tune with the force had. I am sure that everyone can use one, but I would like to see different animations when a Consular uses one vs a Knight. I can liken it to the sport of archery, as an archer myself. Anyone can nock an arrow and pull a bow back. Then there are those who can hit a target and those of us that can zip the head off a turkey at 40 yards.
There are two solid quotes that seem to justify why BW chose to feature the saberstaff for the Consular/Inquisitor. The first comes from one of the "Combat Tactics" videos..
The dual-bladed Lightsaber preferred by many Consulars requires a skilled approach to dueling. Wielding this weapon, Jedi Consulars will draw upon the Force to sense their opponents’ locations and strike them all down with precision.
The second comes from the Wookiepedia entry for saberstaffs / double-bladed lightstabers..
To most effectively wield a double-bladed lightsaber, the staff must be kept moving around the body, never holding still and presenting an easy target, nor a predictable strike. Many users believed that the blades must be under control at all times. That means manipulation of the length or intensity of each blade, either through telekinetic means or physical, both of which are extremely hard to focus on while in combat. Exar Kun is believed to have mastered such a technique.
As far as being limited to just these two classes, there is concept art for saberstaffs in the Holonet entries for both the Jedi Knight and the Sith Warrior, so I'm pretty confident all force classes will be able to use them. The only thing missing for me are the Exar Kun style sabers with the shorter hilt and the ability to only turn on one blade. I can't seem to find any pictures that show this type. However, the large number of traditional style hilts that look identical on either end could mean good things for those folks who would wish to have a Darth Maul style where you can detatch the single hilt into two.