If unbelief 'encouraged' sin, and faith 'generates' righteousness, with being given that not everyone is saved, even though it is made possible that everyone might be saved then it seems to me that pivotal factor, which God would choose, as He so willed, is the choice to believe or not to believe. Aside from that consideration whether choice is the sin or the problematic motor of the sin, if you are comfortable insisting that "all" does not always mean "all" with regard to application of salvation, reasoning that to be left to God's sovereign will, how can they deny the possibility that it may not be God's will to atone for 'all' sin save one?