Why does AlphaZero perform better than vanilla MCTS? [closed]

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I understand main difference between AlphaZero and the classic Monte Carlo tree search is the playout (simulation) step is replaced with a neural network prediction which itself is trained from the output of the MCTS. How does this additional complexity improve the performance?

My guess is that classic MCTS would not perform worse than the AlphaZero's hybrid approach on a system with unlimited memory. Since memory is a constraint in the real world, the neural network is a work-around.