"Recidivism rates for sex offenders are lower than for the general criminal population. For example, a Bureau of Justice Statistics study of 108,580 non-sex criminals released from prisons in 11 states in 1983 found that nearly 63 percent were rearrested for a non-sexual felony or serious misdemeanor within three years of their release from incarceration; 47 percent were reconvicted; and 41 percent were ultimately returned to prison or jail."[1]
There's also the problem that stigmatisation helps more or less no one, because it's unlikely that parents can (or should) effectively supervise their children 24/7. And even if they did, it may protect their children at the cost of others, leaving the overall rate of these crimes unchanged.
To use an example with less emotional baggage: "Watch out for terrorists!" is a similarly useless warning.
Sorry, but it isn't enough for me.