If with some other hashing mechanism it was enforced that the miners had all the information they needed to generate the block themselves, it would discourage pools because any pool member could 'steal' a block.
Incorrect. A block cannot be 'stolen' because it is immutable once authored. Every attempted block has an independant success probablity, and changing any part of the block results in a totally different block.
For clarity, that means you can't solve a block for a pool and then decide the coins should go to you instead. Doing so would give the block a new hash, which would not be valid.