Wall Street’s victory securing new broker conflict-of-interest rules at the SEC is by no means final.

The regulatory overhaul directing brokers to act in their customers’ “best interest” faces potential challenges in the courts, Congress, and inside the Securities and Exchange Commission itself, if a Democrat takes control after the 2020 elections. Investor advocates, Democratic leaders, and state officials eventually may reshape the Regulation Best Interest package a divided SEC adopted June 5.

But success isn’t guaranteed through a court...