I agree completely.
I don't believe we do good works in order to win a ticket to heaven, either. In fact, to put it that way really cheapens Christ's grace, in my opinion.
But, Sojourner, I have heard you state on many occasions that every single solitary person who has ever lived will ultimately be saved. (And you probably know by now that my own belief doesn't differ from yours all that much. I believe that the vast, vast majority of all people will be.) But there is a pretty significant flaw in your statement that "we do good works because, through grace, we are good." If all mankind is saved through grace, why, through that same grace, are all men not good?
I would agree that anyone who is truly converted to the gospel of Jesus Christ will have experienced a change of heart as a result of that conversion, and will have a sincere desire to do good. But all will continue to be tempted, and some will not resist. If being "good" is a natural consequence of grace, why do so many Christians continue to struggle to live the way they know in their hearts they should?