Is there a reason for the anvil and post in a LED having the shape they do - other than making it easier to distinguish between the anode and cathode?
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Both wires are placed symmetrically with respect to the LED's axis. The die is also placed on the axis. Therefore the cathode wire (which holds the die) has to extend towards the center line.
The anode wire is shaped so that you can't pull it out the plastic housing.
The "anvil", as you call it, serves not only as one of the electrical contacts, but also to physically hold the chip, provide some heat-sinking, and provide some directivity to the emitted light (the chip usually sits in a cup-shaped depression). The "post" just needs to have a bonding wire attached to it, so it can be much smaller.