Why not? If I can tell I solved a block, and I can fail to relinquish said solved block, why couldn't I just claim it as my own?
Nevermind... I think I figured out why. The pool would have already dictated the address that the reward would go to.
That is the one reason. The other is that the miner doesn't have the whole block, it only has the header.
These two reasons are sorta related, in that the miner could figure out most of the block by looking at permutations of combinations of pending transactions on the network, but it can't make a coinbase that would let the whole thing hash to meet the solved header unless it already knows the private key the pool used. And if it already knows that, it might as well just wait 100 blocks and race to spend the reward before the pool does.