Actually, rebound is quite important in a proper anvil... If it wasn't, people wouldn't have developed a way to test rebound, or testing for rebound wouldn't be the first thing they do when they look at a new anvil. Also, the best anvils wouldn't have the highest rebound ratings if it wasn't important. Rebound is important because it signifies how efficiently the anvil is opposing the force of the hammer. Rebound doesn't have anything to do with 'bounce' of the hammer or whatever (though that is a common misconception, even among guys that have been making knives for a long time), it has to do with Newton's Third Law, which states that each and every action has an opposing, equal reaction. In this case the action is hitting the anvil or piece with the hammer. The rebound indicates how much of that energy is being reflected back into the work piece. If the rebound is low, the anvil is not returning as much energy into the piece, which results in the slower, uneven moving of metal....
The best way to describe why its important is in this case: If you take a piece of square bar and taper the end by hitting a side, turning it 90 degrees and hitting the other side, you should be able to accomplish an even taper if the rebound is high enough... If not, your taper becomes lopsided, because the hammer is deforming the metal, but the anvil isn't nearly as much. That means with a low rebound anvil, you'd have to flip the piece to all four sides to make it even... This takes longer to do.
Ultimately, the bottom line is that rebound is very important to people who blacksmith daily. If you're swinging your arm all day long, you want the best rebound an anvil can provide, because even if realistically, a proper anvil saves you 10% of the swings in a day because it's high rebound (efficiency), then it's totally worth it. If you are forging one knife a month like most guys here, then it doesn't really matter.