Losing the thing you stood to gain by cheating isn't a punishment, if that were true there would be no consequences to trying to cheat at everything all the time. That's why if you get caught robbing a bank, they don't just take the swag off you and say, "well he's been fined £3m, I think that's already a enough punishment."
The point of the FA investigation is to establish the requirement to issue an actual defined punishment. 'Bad reputation' and 'social media threats' are completely subjective and unquantifiable.