Owen proposes that the subjective genitive reading "would therefore denote the effects of the Law's activity among humankind since the time of the giving of the Law to Israel..." and "would then lie not so much on human failure fully to obey the Law (although that is implied) as on the Law's own inability(owing to the gripping power of sin) to produce in people a righteousness that can survive before the bar of God's judgment." (554)
Owen's argumentation definitely deserves a close read for anyone working on Paul's view of the Law and also those folks who are engaged in the pistis Christou debate. Without much time to reflect, I do believe Owen's reading makes sense of much of the evidence, offering a coherent reading of Rom 3.20, 28; Gal 2.16; 3.2, 5, 10.
Do check it out and let me know what you think.