The difference is significant, because if you discover a way to significantly reduce fraud for a low cost (including cost of freedoms and similar), it will be worth implementating. And there isn't some point where you say "we are already down to x% fraud, we don't want to go any lower than that, even if it doesn't cost us anything".
Don't make it illegal-but-not-enforced. Because then, whoever is in power can selectively enforce the law against any group they choose.
I can't think of any resonable society that have taken actions to show that they want the probability to be 100%. I would even argue that the most harsh dictatorships probably have the highest enforcement, but that laws were/are very selectively enforced in the favor of e.g regime officials.
Especially if we broaden fraud to include other crimes. There are costs to prevent other badness in society as well. Firstly it's the cost in taxes/allocating resources to its prevention: Do we really want to allocate a really large chunk of our shared human capital to police marginal criminal activity? How much more polices, judges, attorneys, lock makers, etc would we need to stop the last bike theft?
Secondly and arguably more importantly is the cost of freedom. A lot of the digital surveillance initiatives that are discussed and dismissed here on HN are enforced in the name of zero tolerance against (really bad) badness in society.
I think its hard, or impossible, to create a somewhat large society with zero crime rate. At least if we still want even just a sliver of the freedoms we are accustomed to in liberal democracies.