That was an interesting Planet Money episode.
From the interview, it sounds like the DOGE employee (Sahil Lavingia) joined up based on the assumption that government departments weren't already trying to modernize their IT infrastructure and fight fraud. In his case, he discovered that the VA was modernizing and preventing fraud, but it was hard, and time consuming.
It sounds like Dunning-Kruger at work. Musk and co think they know IT, so it should be possible to waltz into a large organization, throw some opensource/AI projects at it, and save a tonne of money. When they get inside, they discover that the systems are really complicated, and that there are existing initiatives to do exactly what they want. It turns out that most of the easy wins have already been won, and it's only the hard tasks that are left.
It's an interesting counterpoint to the modernization program that was started during Bill Clinton's term. They took years to understand the systems they were trying to improve, and built incentives for people inside those systems to propose improvements.