What advantage does it provide vs not withholding? If you don't keep your first block secret and find a 2nd block, you get the same rewards. On the other hand,

What advantage does it provide vs not withholding? If you don't keep your first block secret and find a 2nd block, you get the same rewards. On the other hand, if someone finds a block while you're keeping yours secret, it's very likely you'll lose the reward of your block. So, you get a chance to discard the block of another miner, but you have to put your own block at risk of being discarded. Maybe there's a gain here, but it's not clear.