We can still blame the propaganda for helping make the laws appealing and getting them to pass

The first true "three-strikes" law was passed in 1993, when Washington state voters approved Initiative 593. California passed its own in 1994, when their voters passed Proposition 184 by an overwhelming majority, with 72% in favor and 28% against. The initiative proposed to the voters had the title of 'Three Strikes and You're Out', referring to de facto life imprisonment after being convicted of three felonies.[4]

And given the popularity of things named after people like "Laura's Law" or "Megan's Law", it wouldn't surprise me if the popularity was due to the rhetorical effect on the average voter.

I think further investigation would reveal that is at most a Western cultural thing, not a hardwired human universal. Elsewhere in time and place, 4 has been the important number -- e.g. recurrences of 4 and 40 in the Hebrew scriptures; the importance of 4 and (negatively) 8 in Chinese culture, etc.. Possibly some other digits have performed similarly in other places as well.