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.
I see where you’re coming from, but would like to add some nuance (not everywhere is like the US).
As a general rule, I think penalising malicious fraud (i.e. fraud not committed out of dire necessity, but in order to scrape an extra buck) is worth it on a societal level, even if the economic benefits aren’t a net positive. It’s about sending the message that we live in a society where people need to treat each other fairly, and where we can trust the system to protect us. Even if society as a whole loses money going after some of this fraud, it can mean an enormous amount to the individuals that have been exposed to fraud to know that society has their back.
On the second level, there’s welfare fraud. First of all, we definitely have a more generous welfare system where I’m from than what’s found in the US, and I think that’s a good thing. We also have some issues with people that are capable of working, or who do work under the table, who still claim benefits they aren’t qualified for. The major issue I see with it is this: By gaming the system, these people in the long term threaten to make the system unsustainable, thus stealing resources and putting pressure on the people the system is actually designed to help.
In a way I see actual welfare fraud (i.e. people with more than enough resources gaming the system to pull government money they don’t need) as worse, because they’re violating the trust of a system society has put in place to help the most exposed among us. This kind of fraud indirectly impacts the least resourceful (possibly a poor translation) people in our society.
In either case, I think the social element of fighting fraud is worth it, even if it is a net negative economically. Fraud in general is a severe violation of the social contract we live under, and “letting it slide” contributes to eroding peoples trust in both each other, and the social system as a whole. It’s worth spending some money to prevent that.