Federal agencies are regularly audited - internally by their own inspectors general, and externally by the Government Accountability Office (GAO) - and most of those reports are publicly available. There are numerous checks on these agencies including management by the president, who can typically fire at will, and oversight by Congress.
Like him or not, Elon Musk is not an auditor, has no relevant experience or expertise and is deeply compromised as he profits from large federal contracts. Giving him unchecked power with no accountability is not the proper way to shine a light on fraud, it's a way to get more of it.