In both cases there's 3 possible outcomes:
1) Google, after reviewing weak and/or zero evidence, backs down and restores the account upon receipt of notice of intent to pursue legal action.
2) Arbitration happens and Google is ordered to back down, restore the account and pay Dad's representation fees.
3) Arbitration happens and Dad loses, which yes would be quite costly.
Only #3 is a gamble, and it seems like Dad has a lot of confidence #3 isn't even a remote possibility. So why would you not pursue legal action?
Given how much attention Dad has received over this, it would be surprising if free representation wasn't throwing themselves at him by now too. Regardless, this is indeed how the legal system works for disputes. He should use it if he really is innocent.