I agree with your reasoning. I also agree with your implicit perspective that this isn't needed at all, and that on balance it is more likely to cause harm than good. I would expect the number of people who feel unable to express themselves, or are threatened with prosecution, or are actually prosecuted inappropriately, would significantly outweigh the number of people who this law should cover and are prosecuted.
It's hard to assess the relative harm. I'm inclined to heavily weight the harm to those whose free speech is impinged, and to relatively lightly weight the incitement, as in my mind someone who is that far over the line that this could/should catch them will likely also be committing all sorts of other crimes that are already covered in our legislation. I.e. a small number of instances where we don't do a lot of incremental good, a large number of instances where we do substantial bad.
It will be interesting to see how this proposal develops. In some sense I'm like you - I'd rather the proposal stay more obviously bad so that it can be more easily resisted. If it gets softened then perhaps people will say "that's not so bad", and we get slow erosion of important rights.
The serious fraud office perhaps? They deal with serious and political crimes, and there's arguably fraud here. A quick read of their website says their remit is largely financial, but you never know.