I don't remember the source but I do recall findings that the costs of investigations into welfare fraud in Germany significantly outweigh the (potential) costs of the fraud itself.

Of course the inefficiency is difficult to prove because it's impossible to correctly measure the amount of fraud that would exist if there were no investigations (the existence of the investigations might discourage fraud in the first place).

Still, it seems pretty intuitive that welfare fraud isn't actually as big a problem as people tend to think. Welfare fraud is one of these problems that are easy to exploit for public outrage. It's relatable ("they steal my (tax) money"), the people doing it are already stigmatised (if you're on welfare you either did something wrong or are simply not trying hard enough), the falsely accused are unlikely to retaliate, it's easily actionable (just add more inspections or simply reduce the benefits) and it's difficult to measure and nearly impossible to solve.

Sure, it may be a non-issue but it so wonderfully exploitable if you're a politician (or a "newspaper" that needs some inciteful headlines).