I ask because we had a situation in Ireland just like this many years ago. It was for welfare fraud specifically and faced criticism for a few reasons. One was that the suspected levels of fraud may have been much lower than the politician was claiming. The other reason was that the cost of tackling it could likely outweigh any savings.
It really depends on what the fraud is, who it impacts, and how severe that impact is.
At one extreme, let’s say that someone is defrauding random citizens of a few hundred bucks a pop, and it would cost a few thousand a pop to reduce or eliminate it, that’s worth it because the few hundred can have an outsized impact.
If someone is committing welfare fraud, until it’s enough to prevent the system from working, then the cost has to be much closer to or lower than the amount stolen because it’s better to let fraud slip through the cracks rather than people.
It can be worth it, even if the cost is higher, but it would need to be a long term solution paid once, or it’s just an added cost of running the system rather than an actual fix. No point in implementing an expensive system change that doesn’t eliminate the cost of the fraud entirely.