You say you are providing context, but what you really do is quote Dick the Butcher's line and then provide a conclusion that is straight out of ABA propoganda.
The line operates as a literal joke on one level. Undoubtedly, a Shakespearean audience would have laughed at it, just as a modern audience laughs at many lawyer jokes. (e.g. What's the difference between a rattlesnake run over by a car and a lawyer run over by car? There are skid marks in front of the rattlesnake.) There was considerable injustice, including punitive taxation and propery seizure measures associated with Henry VI's reign, so it is possible that Shakespeare was making an historical point about lawyer complicity in the corrupt practices of Henry VI (though Shakespeare can be fast and loose with his history). So, the killing of lawyers line could easily be a metaphor for the triumph of justice over a legal system that was not delivering it at the time.
The Dick the Butcher line is part of a dramatization of Cade's Rebellion, which in many ways was sort of the Libertarian tea party of its day. Basically, Cade led a bunch of minor gentry who thought they were being overtaxed and treated unjustly in the legal system by Henry VI's regime.
I don't think Shakespeare was advocating killing lawyers, but he is not making the point that lawyers are all that stand in the way of chaos -- particularly not in the context of Henry VI.
in context. Henry VI, Part II, Act IV, Scene II
Dick tells Cade "The first thing we do is kill all the lawyers."
Why? Because when you're fomenting revolution those that know the law are best quickly dispensed.
