Some Democrats in Trenton think they’ve found an answer to New Jersey’s problems: a new government-owned bank.

Gov. Phil Murphy, formerly of Goldman Sachs , campaigned last year on the idea of creating a bank owned by the state and its municipalities. “A public bank will allow New Jersey to invest in New Jersey,” Mr. Murphy said. He added that it would “provide capital to communities that, for too long, have been ignored by the financial system, whether they be women-owned businesses, businesses owned by people of color, or small businesses with big ideas.”

At the beginning of this year’s legislative session, two Democratic state senators introduced the State Bank of New Jersey Act to turn Mr. Murphy’s campaign proposals into reality. The new bank would be run by an appointed board, plus the state treasurer. It would be instructed to make its services available to all public entities, and it could enter into real-estate projects using the power of eminent domain. The bank would also be empowered to extend student loans and small-business loans.

For years progressive groups have advocated government-run banks, arguing that they would serve local users better than private banks do. A model often cited is the Bank of North Dakota, the only state-owned bank in the U.S., which was founded nearly a century ago as part of a populist farmers revolt. It has survived as an apparently functional part of the economic landscape in one of the nation’s most conservative states. Another oft-cited example is Germany’s Landesbanken, a group of state-owned regional banks known for midlevel commercial lending and for overseeing local savings banks (Sparkassen) run by municipalities.

As private banks see it, state-owned banks succeed, if they do, because of unfair advantages. They’re exempt from taxes, which may or may not be partly offset by an expectation that they return money to state or municipal treasuries. Public banks can also raise money at the lower interest rates charged to government borrowers, since they’re seen as unlikely to default (and likely to be bailed out if they do).

But you don’t hear as much favorable buzz about the German Landesbanken as you used to, given their recent performance. The Economist reported in 2015 that “this hybrid public-private model, which relied on public largesse in days past, has fared disastrously since the financial crisis.” The promise that politically controlled banks would choose investments on a sound business basis has proved false. “State politicians sit on the supervisory boards, enjoying playing the role of banker, supporting favored projects and soft loans to companies that employ lots of voters,” the magazine noted.

Alert readers might have noticed what Germany and North Dakota have in common: relatively clean, honest political cultures. Germany regularly ranks among the 10 or 20 least corrupt countries in the world (and ahead of the U.S.). Among American states, the measures vary. North Dakota has had more corruption convictions than one might expect, but it still scores well on most outcome-based measures. New Jersey, on the other hand, fares quite poorly.

A 2014 study by the Safra Ethics Center at Harvard ranked state corruption by surveying political reporters covering capital politics. North Dakota was in a small group of states where illegal corruption was perceived as “not at all common.” When it came to “legal” corruption—i.e., the kind that isn’t against the law but is still aromatic—the study found it was only “slightly common” in North Dakota.

On both metrics New Jersey was among the seven states perceived as most corrupt. The Soprano State has provided America with some of its gaudiest and most colorful political double-dealers, with mayors in Atlantic City, Camden, Irvington, Jersey City, Newark, Orange and Trenton all having been convicted over the past generation.

A State Bank of New Jersey would be unlikely to content itself with the predictable and repetitive lending that goes on in an agriculture-and-extraction economy like North Dakota’s. It would inevitably turn into a Favor Bank for politicos hoping to lure subsidized jobs from the more vibrant cities of New York and Philadelphia. Once the initial buzz of idealism passed, it would become a tempting honey pot for the corrupt politicians for which New Jersey is famous.

In that sense, a State Bank of New Jersey really would be sure to create jobs—for prosecutors.