Corporate liability insurance in the US, which is also a very common thing to get, often does not cover your defense against "intentional torts" such as defamation or fraud. It usually covers things like slips and falls, product-related liability, etc. I would be surprised if your German version covers defamation.
I live next door and have some legal insurance, but you need to pay attention to what coverage you get, because you need to select what categories you want coverage for; vehicles (e.g. if someone who caused an accident refuses to cooperate with you), consumer/housing disputes, work and salary, taxes / stocks, family issues like inheritances, second homes / real estate, etc etc etc. And of course, you can't take out insurance for an ongoing issue, it doesn't cover criminal cases (when you did a bad), business cases, etc.
Germany also regulates legal fees, so self-insurance is quite reasonable. I've now been involved in two cases (once as plaintiff, once as defendant) and it seems the amount I paid is approximately the same as I would have paid in legal insurance.