We can, of course, study cases where the Court tried to substitute for a genuine popular movement. Brown was not one; black Americans had carried the idea of integration forward for nearly a century by the time the Court concurred. By contrast, in 1973, the Court decided Roe v. Wade, which leapfrogged ahead of public opinion to “settle” the issue of abortion, setting forth a detailed framework for its regulation in virtually all cases. Abortion-reform movements were stirring, and succeeding, in some states in 1973, but the issue had not been widely aired or made a focus of mass concern. Certainly there was nothing like the movement against school segregation or child labor. The country was feeling its way, and the Court stepped in like an officious parent to “settle” an issue not ripe for settlement.
This is an argument I've addressed at interminable length elsewhere, but there are a number of fundamentally erroneous assumptions here. First, as Marcotte says, the backlash to Brown was substantially more severe than the backlash to Roe; Richard Nixon didn't have to send the Screaming Eagles into Texas to force the state to open abortion clinics. Second, the Supreme Court didn't "leap ahead" of public opinion; it has always been supported by national majorities. And third, and most important, Roe did not in any way create the pro-life movement. As Linda Greenhouse and Reva Siegel explain in a superb new article, the pro-life movement was already sufficiently mobilized at the state level to have stopped the abortion reform movement dead in its tracks.
Epps is definitely correct that courts cannot end conflicts over contested social issues, and it didn't do so in either Brown or Roe. But there's also no evidence that changes obtained through the courts produce more opposition than changes obtained through other venues. The backlash against abortion rights was inevitable. Had the Court not intervened, woman's access to abortion rights would be even more restricted than it is today.