>The problem is that merely insulting someone can be a crime at all
I disagree that this is a problem per se. Pretty much all jurisdictions across the world have laws like that. It really depends on how exactly the law is implemented.
In fact, American libel and defamation laws are, in some ways, more problematic than many European ones simply because of how the legal system works. If you are sued in a place with no SLAPP laws, the mere lawsuit can be so expensive that it can have a chilling effect on free speech, even if the defendant ultimately wins the case.
(I do agree that laws singling out politicians are stupid.)
https://www.dw.com/en/germany-greens-habeck-presses-charges-... (scroll down to explanation).
its not the only European country where this is possible, at least in theory: https://www.politico.eu/article/european-countries-where-ins...