At first I though this was a bit draconian; that is, solving what is largely an education/misinformation issue and diminishing civil liberties all the while opening the door to abuse from a more nefarious government — on the other hand, it would force the topic of vaccinations into a court of law where anti-vaxx fallacies would fall completely flat.
Personally I'd much rather bring up charges against the primary sources of such misinformation; then that might cause them to think twice about spreading lies in the future.
But America is open for business when it comes to grift. From Alex Jones and Joe Rogan to Steve Bannon — they understand that the gullible are profitable.
The problem is with primary souce is that for all intents and purposes there isnt one anymore. Sure back in the 90s there were but its a lot like creationism, a rat king of lies and stupid shit. Self perpetrating bullshit has to be dealt with via other means.