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The idea is that even there's a policy network that is able to decide at some point what the best possible move is, the tree search is done to refine this choice and to "evaluate" it. This is why a value network is derived from policy network and is used in conjunction with MCTS to make sure that the moves AlphaGo picks are good ones.

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It is necessary to make multiple alternatives in the tree comparable in an easy way (and nothing is better comparable than scalars). They could also go about training a network that compares two positions to decide which one is superior, but that would require much more computation. Or another alternative would possibly to learn the value somehow jointly with the action selection, but that would possibly also be harder both to train and evaluate.

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