I believe the whole point of pretraining on reference policies, which a collection of "optimally" played human games is, is just avoidance of bad local optimum.
It can be a case that training and learning on just a learned policy is going to get you stuck in a local optimum that is of worse quality than the one with pretraining.
If they stored all of the AI played games their reference policy (the data) would be of extreme value. You could train a recurrent neural network, without any reinforcement learning, that you could probably run on a smartphone and beat all of the players. You wouldn't need a monte carlo search too.
There are algorithms [1] that have mathematical guarantees of achieving local optimality from reference policies that might not be optimal, and can even work better than the reference policy (experimentally) - assuming that the reference policy isn't optimal. The RNN trained with LOLS would make jointly local decisions over the whole game and each decision would guarantee that a minimization of future regret is being done. Local optimality mentioned here isn't finding a locally optimal model that approximates the strong reference policy, it means that it will find the locally optimal decisions (which piece to put where) without the need for search.
The problem is that for these algorithms you have to have a closely good reference policy, and given a small amount of human played Go games, reinforcement learning was the main algorithm instead, it allowed them to construct a huge number of meaningful games, from which their system learned, which allowed them to construct a huge number of more meaningful games, etc.
But, now when they have games that have a pretty good (AlphaGo is definitely playing on a superhuman level) reference policy, they can train the model based on that reference policy and they wouldn't need a search part of the algorithm at all.
The model would try to approximate the reference policy and would definitely be worse than AlphaGo real-search based policy, but it wouldn't be significantly worse (mathematical guarantee). The model is trained starting from a good player, and it tries to approximate the good player, on the other hand, reinforcement learning starts from an idiot player, and tries to become a good player, reinforcement learning is thus much much harder.
[1]: http://www.umiacs.umd.edu/~hal/docs/daume15lols.pdf