Those are arguments about shaming _inside_ parliaments and courts, which are obviously controlled speech environments; that has limited effect _outside_ courts, with the exception of sub judice rules.
> well developed traditions against name-calling and insistence on respectful language and behaviours like using proper titles (which can be a bit off-putting seeing how politicians act outside parliament)
Indeed. You can call your opponent a terrorist criminal just fine as long as you step outside the building first.
For a given dispute the court is certainly more likely to find a just result .. if you can afford to litigate. Or, in the case of criminal law, if the prosecutors will prosecute. If they won't, you can only resort to "the court of public opinion", i.e. shaming.
The two main tools the parliaments use is regular, time based election cycles combined with very formal procedures making sure everyone gets a chance to speak. In the ones I'm more familiar with (Australian, British, probably American) they also have well developed traditions against name-calling and insistence on respectful language and behaviours like using proper titles (which can be a bit off-putting seeing how politicians act outside parliament). If a politician has a solid faction backing them they can get away with some pretty extreme stuff and just shrug off the criticism. Trump is a more interesting case study, but realistically anyone in modern politics has to wade through a tide of abuse to get anything done. It is all but impossible to stop a politician getting a message out and sticking by it if there are votes to be had.
The main tools the courts use are having professional and emotionally unattached advocates who are aligned with the people they represent (aka lawyers) and extremely developed rules of evidence that strip out opinion and personal standards in an explicit quest to work out the facts and make sure any punishment is consistent with the law.