Before you jump to evolutionary algorithms, note "The Problem with Evolution" section in the OP. This was written by a guy who knows what he's doing with evolution, and it's interesting to see him turning to MCTS given his previous success with evolution.

The gist is that games are fragile with respect to mutations (motivating the need for a search paradigm not based on gradualism). This fragility may not exhibit itself as strongly for the parameter tweaking involved in the balancing problem, but balancing quickly shades into general game design when you start to consider non-trivial tweaks.