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 would say probably yes, because if you leave something like that unenforced, people learn that they can get away with it and the trend spreads.
Sure the enforcement might cost more than it saves today, but it quite likely might cost less than it would cost once the problem expands 5-10 years from today.