In Miller-El v. Dretke, 545 U.S. --, No. 03–9659 (June 13, 2005) the Court grants habeas relief to petitioner on his Batson claim. Justice Souter wrote the Court's opinion. Justice Breyer wrote a concurrence in which he posits that peremptory challenges should be done away with altogether. He seems to be worried about preservation of the democratic institution of the jury when he states
[...] If used to express stereotypical judgments about race, gender, religion, or national origin, peremptory challenges betray the jury’s democratic origins and undermine its representative function.
Of course, when he dissented from Booker's merits opinion and drafted Booker's remedial majority opinion, Justice Breyer's concern for the institution of the jury was nowhere to be found. While there is no doubt that peremptory challenges can and are abused from time to time, I would hate to have to try a case in which there were no peremptory challenges. What you would get is likely more background checks on jurors by the government in attempts to find for cause challenges, with the defendants in most cases not having access to this sort of information. See our post on this here.