That would be a waste of resources given the chances of a real criminal testing his/her password strength on a government-operated website are very remote. Even then, they would have to invest in marketing to get people to actually use it when, we all know now, the GHCQ/NSA can simply collect everything at critical infrastructure points.
You think they're after "real criminals"? Tell me, what is this "real criminal" of what you speak? Is it someone who disagrees with the edicts of the state? Is it someone who has the wrong skin colour?
Occam's razor says you're right, but while they're busy accusing us all of criminal acts, we may as well do the same.
This looks like a good idea, poorly executed.