No individual needs to believe in
the Church to do what is right. In fact, there are a great number of atheist who are far more holy than a great number of Catholics.
But morality wants to change like everything else.. and it's not always for the better.
So it's not just white noise. Without the church good and evil are relative; distasteful to us but not objectively awful and subject to corruption and drift. Human beings are capable of all sorts of morality (slavery, rape of women, children ). Is it not the church that says the dignity of every human being is worth something? Isn't this why the crimes She's accused of her so awful and hypocritical ?
But if we burn her down completely, why should we keep her morality? Why shouldn't we revert back to a more sensible rule of morality we're human beings are property of the powerful? Why should the Christian morality we largely have adopted be the one we keep?
You are correct when you say you need religion to make good people do evil.. but when you burn it all down, good and evil are just social constructs without any sort of anchor; they are simply meaningless statements to evolve with our cultures.
The answer must be to purge the church and not its morality.