On Tuesday a federal judge ruled that Detroit was eligible to enter Chapter 9 bankruptcy – the largest municipal bankruptcy in American history. That same day, we got a price tag for how much the collection of the threatened Detroit Institute of Arts (DIA), one of the country's oldest and best museums, is likely worth. DIA has been under threat for months since Kevyn Orr, the emergency manager appointed by Michigan governor Rick Snyder, insisted that everything in Detroit is "on the table". For months, salivating creditors have circled the museum while the institution has tried to keep them at bay. Now, for better and for worse, we have a price tag.

In a five-page letter to Orr (pdf), the auction house Christie's appraised the works of the DIA collection that the city bought at $452m to $886m. It's significantly lower than the $2bn figure batted around this summer. More than that, it disguises the fact that a few masterpieces now on public view, among them Pieter Bruegel the Elder's Wedding Dance and Matisse's The Window, account for as much as 75% of that estimate; selling forgotten pictures in the basement is not going to have an impact.

The pitifully simplistic justification for looting the DIA goes like this: Detroit owes money. Detroit owns pricey paintings. (The museum is unusual in that it's owned by the city, rather than by a nonprofit foundation, though that could change.) Therefore, Detroit should sell up to pay its creditors.

Contained within that malign logic, though, is a morass of assumptions, mistakes, and flat-out lies. Most of the paintings in the collection are tied up in legal agreements that make deaccessioning impossible. A fire sale of dozens of major art works would also likely cause a depressed market; even in these go-go times for the art market, there are limits. Then there are the costs. Even a small sale, in fact, would have immense ramifications. Putting just a handful of artworks on the block would lead to a mass exodus of philanthropic donors, who would be justifiably unwilling to throw money towards an institution that can't guarantee the preservation of art in perpetuity. It would also wipe out around $22m in tax revenue DIA has enjoyed since three Michigan counties voted last year to support the museum through a property levy.

This is not to mention the regulations governing American museums, which expressly forbid the sale of artworks for any reason other than to acquire other artworks. Or the UNESCO treaties such a sale would violate. Or the opinion issued this summer by the Michigan attorney general (pdf), which explicitly stated that such a sale would contravene the law. This is not even to mention the insanity of treating artworks in the public trust as mere assets.

Even putting all that aside: on the barest economic level, raiding the museum will have no meaningful impact on the city's bottom line. Detroit has $18bn in debt. More than 100,000 creditors have swamped the city. The Chapter 9 process begun this week means that the city can renegotiate all of its contracts – a process that need not lead to pension cuts for public workers if done right – and it's those renegotiations, rather than a frantic search for the most appealing baubles in city limits, that will get Detroit back on its feet. As Graham Beal, the bowtie-favoring British director of the museum, told the New York Times:

I'm an old European socialist. I would do anything I could for pension-holders and their problems. But those problems have nothing to do with the DIA.

I am not such a romantic that I ascribe to art the mystical status of some of the DIA's defenders. If there really were a one-to-one correspondence between selling off paintings and feeding families, I could become a museum looter myself. But the whole point of a bankruptcy is to solve deep and structural problems in the economic organization of a major city – not to strip-mine everything from the Bellinis at the museum to the baboons at the Detroit Zoo for however much one-time cash you can squeeze out of them.

The judge in the Detroit case recognized this in his decision on Tuesday (pdf):

When the expenses of an enterprise exceed its revenue, a one-time infusion of cash, whether from an asset sale or a borrowing, only delays the inevitable failure, unless in the meantime the enterprise sufficiently reduces its expenses and enhances its income. The city of Detroit has proven this reality many times.

Detroit has serious problems, but the Detroit Institute of Arts is not one of them. It's running very well, actually; the museum is run at no cost to the city, and to disembowel one of its few great institutions for the sake of dysfunctional ones defies not only decency but logic. Remember, we are not talking about liquidating an insolvent company here. This is the 18th largest metropolis in the United States entering bankruptcy, a city plagued not only by crime and mismanagement but by rapacious financial interests more than happy to let the Motor City crumble.

And just as Detroit is not a corporation, the Detroit Institute of Arts is not a family or a small business fallen on hard times – it's a public trust. Now is the time to remake Detroit, not to strip-mine it.