Can a regulator deny key services to a bank merely because it doesn’t like its novel business model? That’s the question in a lawsuit filed in federal court recently by TNB bank, which claims the Federal Reserve Bank of New York is shunning it out of existence.

James McAndrews, who worked at the Philadelphia and New York Fed for 28 years, co-founded TNB after spotting an opportunity for arbitrage in interest-rate disparities. Since 2008 banks have received billions of dollars in interest payments from their excess reserves...