the Crown sometimes forgets their duty to act in the public interest and can pursue a case where those involved on both sides do not personally want to pursue a legal dispute.
That is not even remotely what “public interest” means. A conflict between two drug dealers would almost certainly not have either side wanting to pursue a legal dispute, that doesn’t mean the Crown is not still obligated to pursue the case, as it is DEFINITELY in the public interest. This has nothing to do with whether the involved parties are interested in pursuing it, although it can in practice make it much more difficult. But this is actually about whether it serves the public interest to address the alleged crime. While you may argue that it does not in whatever case you are imagining, you very probably legally incorrect, and maybe a bit biased too.
The other two points I would generally agree on in many cases, but I would also point out that in just as many cases the complete opposite is true. The system is very imperfect, unfortunately and no obvious solution appears before me.
What Carney says publicly doesn’t always seem to reflect what Carney is actually doing behind the scenes. Unfortunately, I understand why Trump’s childish reactionary politics make such dishonestly and subterfuge necessary because we are very vulnerable to his tantrums, and enduring his petulant tantrums is counterproductive to the effort of actually getting us to the position where we no longer have to suffer from his tantrums anymore.