I can see where you're coming from here, and I agree no system is perfect, but in the UK the reporting restrictions come into play as soon as an arrest is made and charges are likely. To me, this makes more sense than allowing media reports then limiting your jury selection to the terminally uninformed.
I suspect the US already has laws that limit press freedoms in criminal cases. Can the American media name a rape victim, for example, or a child involved as a witness? Any step away from freedom of speech should be taken with care, but IMHO, this one would be a step in the right direction.
ETA: Once again, I hope this doesn't come across as a nose-thumb about our system being better than your system. I think the UK could learn a lot from America's libel laws and separation of church and state, but sub judace is something I feel we Brits have got right (or at least mostly right).