Then have the money go straight to some uncontroversial charity. Facebook still benefits by the reduction in frivolous support requests, perhaps making this a feasible option.

> That would lead to people claiming FB bans accounts to make money.

More realistically it probably would lead to FB banning accounts to make money. Theoretically you could setup the incentives such that money from banned accounts can only go towards paying moderators though I'm not sure if anyone would believe you.