It's only a deterrent if people think they might get caught and punished in a way that would negatively affect them. Like speeding, people speed as they know the chances of getting caught are low, and if they do it's a £100 fine, 3 points (that don't affect anything) or 4 hours on a speeding course. Watch speeding disappear overnight if instead of what it is now, anyone caught got 10 years in prison and there were cops on every street with speed guns.
Same with this, people would know it wouldn't get investigated so nothing would happen, so they wouldn't care.
Don't still see any harm on reporting these, some might don't want even that happening. If somebody would try to scam me with forged documents, i would report it even it would be 99.89% sure that it wouldn't get investigated. Assume police would need to take that report even they wouldn't actually do anything further.