They work pretty well on bolts that broke off due to overtightening. Rusted in and broke off because they are stuck... That's another story.
I've had real good luck over the years building up a post of weldment on the broken stud/bolt, providing it is in a cast iron block. Build up a post, and then back it out by gripping with a locking jaw plier, or weld a nut onto it. The many short spot welds required to build a post seem to put enough heat-cool cycles on it that the bolt remnant is no longer frozen, and the hung up stud comes out.
There is a lot to be said for just using a left-hand drill bit, too. Size it big enough to miss the thread of the block, and drill away! At some point, the stud usually unscrews and comes out clean with most of the threads cut off. Of course, that is presuming you can lay hands on a good left-handed drill bit of the right size.
Besides, the name might suggest that they are for Easy-(to get)-out broken studs.