Why shouldn't journalists be subject to statutory regulation?

There are lots of sacred rules that govern our society.  For example, we require lots of important classes of people to be independent, and crucially to be free from political interference.  For example -  Judges, Chief Constables, Barristers, Her Majesty's Inspectors, Doctors etc etc. None of them however, is free from statutory regulation.  Their powers, duties, conduct, ethics and the enforcement of these derive from statute, (or from common law which could easily be replaced or amended by statute).  The Lord Chief Justice (and to some extent the Lord Chancellor) disciplines and regulates the judiciary, pursuant to statutory powers.  Doctors are disciplined and regulated by an independent regulator created by statute and itself regulated by HMG via the Privy Council (that's the body which advises HMQ to grant Royal Charters - before anybody gets excited about using a Royal Charter to set up the new press regulator).  Barristers are about as fearlessly independent as professionals get, but are regulated by an independent body which finds its powers and its own regulation in statute.  Why has statute been used to regulate these important independent entities? Because it is important:  The role of law is primarily to facilitate a peaceful and cohesive society by rhetorically stating that bad things are bad and providing the State with coercive powers to prevent and punish bad things and those who do them.  The Leveson Report has catalogued lots of bad things which journalists (and others) have done. A lot of those bad things can already wind you up in a criminal court.  To that extent journalists are already subject to the statutory regulatory control of the criminal law.  It is clear that such minimal regulation is insufficient.  Some strong medicine is necessary.  Bad Judges, policemen, barristers, doctors etc are dangerous, they can kill people or at least destroy or damage lives, livelihoods and property. That's why statute permits independent regulators to investigate and expurgate such malefactors. Turns out that bad journalists can also do bad things with similar consequences.  Why shouldn't such bad journalists be investigated, adjuged and thrown out of their profession?  Why would such a statutory system inhibit the fundamental freedoms of the press any more than the ability to discipline a judge, strike off a doctor or hound a bad Chief Constable out of his job inhibits the freedoms and independence of such important lynch pins in our society.  The professional rule which prevents me from misleading the Court (lying) keeps me on the ethical straight and narrow - but it does not inhibit my treasured professional independence. An ethical rule which required journalists to have some shred of evidence before publishing, would not curtain their freedom to publish once they had some evidence on which to base their story.  We are talking about a basic code of ethics; something every profession should have and where the profession has an impact on society, the enforcement of that Code must be by a statutory mechanism. The claim to immunity from statutory regulation currently being made by journalists is unsustainable and unsupportable.  Their claim to freedom is of fundamental importance to our freedom, without them, our freedoms would wither.  But their freedom does not extend to a freedom to do bad things with impunity - they are as subject to law and to its regulation as the rest of us.  Journalists have a right to write and be free from censorship and from political interference; but they have no right be free from and to be above the law.  They would be the first to launch into a scathing headline on the front page if another profession claimed such an immunity; they have no privilege from such criticism.   

In short, Leveson needs implementing in full and quickly.