I think it's a good thing this has been made an issue. Peterson has said this was the way he was raised and he did not know it was wrong. There are probably a lot of parents out there who think this way, now they are at least being exposed to the idea that this is not acceptable in our society, that there are better ways to discipline a child. It's easy to get frustrated and lash out physically, much harder to come up with better solutions, people have to know the better options out there.
Peterson has not lost his job, he is merely been suspended. He will take a financial hit, but it's not like he is going to be living on the streets, as a professional athlete he will still make ungodly sums of money. It's probably more of an issue for him that he is missing the season, plus the damage that has been done to his reputation, but his fans will forgive him and he will come back from this and probably be a better person and a better parent.
Did the NFL go too far? Maybe, but better to err on the side of protecting defenseless children than on the side of wealthy, entitled athletes.