We have quite a lot of public stats on the insurance companies in Denmark. You can see how many formal complaints a company have received, I.e. customers who have made a complaint a decision made by the insurance company, how many of these complaints have been in favor of the insurance company or the customer, which types of insurances each company gets most complaints about, etc. So there is a lot of data that allows you to make a informed decision about which insurance company you want to choose.

And even on the off chance they actually pay for whatever you need, you need to go through an ungodly amount of bureaucracy and most certainly pay a deductible as if you are not already paying enough for the insurance!