Elon Musk’s cost-cutting bonanza appears to be having less impact than the world’s richest man is claiming, with a review finding that almost 40% of the federal contracts scrapped so far will save the American taxpayer not a penny.

The Associated Press put under the microscope a list of 1,125 federal government contracts that Musk’s “department of government efficiency” (Doge) boasted it had torn up in the first month of the new Trump administration. The news agency found that of those, 417 were likely to produce no savings to the federal budget.

The shredded contracts had been flaunted by Doge on its “wall of receipts”. Yet in many cases the money had already been spent, or had been legally committed to the extent that it was too late to recoup the funds.

“It’s like confiscating used ammunition after it’s been shot when there’s nothing left in it,” Charles Tiefer, an expert on government contracting law, told the AP.

The review is just the latest investigation suggesting that Musk’s stampede through federal departments in an attempt supposedly to uncover fraud and reduce waste is not having the benefits claimed for it. One of the cancelled contracts was listed on the “wall of receipts” as being worth $8bn, when in fact the New York Times discovered it was valued at $8m.

Musk’s latest ruse, demanding that more than 2 million federal employees all email Doge a list of their five weekly accomplishments or face dismissal, has caused mayhem across the US government. Several Trump-picked heads of department have openly resisted the move.

Kash Patel, Trump’s choice to be director of the FBI, instructed all employees at the bureau to “pause any responses” to the Musk edict. But late on Monday the Doge supremo was keeping at it, telling federal employees that if they failed to respond to his request a second time it would “result in termination”.

Now awkward questions are beginning to be asked by federal judges about whether Doge, and Musk’s role within it, are even lawful. At a hearing in Washington DC on Monday, during a lawsuit over whether Musk’s team of disrupters should be given access to sensitive treasury department data, a federal judge raised concerns about the constitutionality of Doge’s “structure and operation”.

Colleen Kollar-Kotelly pointed out that under the appointments clause of the US constitution, federal agencies are generally run by officials appointed by the president but subject to confirmation by the Senate – which Musk has not been.

The judge grilled government lawyers about Musk’s role and the authority that underpinned it. A government attorney, Bradley Humphreys, replied that he had no information about the billionaire’s standing other than that he was a “close adviser to the president”, Politico reported.