What do you mean, pay double? If you mean that, with regular employment, your "employer pays half" - that is just an accounting trick and you actually pay all of it.
You pay twice as much as regular employees, whose employers cover half of it. It's not an accounting trick, since the half the employer pays is not included in your net income. The same applies to public pension payments, although freelancers can opt out of them.
> since the half the employer pays is not included in your net income
There is a total cost for employer for a particular employee and the take-home pay for that employee. Where between those two we put a number that's called "your net income" is just arbitrary convention.
Employer knows how much the total cost will be when they negotiate the salary. It's all the same to them if the entire amount goes to you personally and then you use it to pay health insurance, or they first pay some of that amount to health insurance and then give the rest to you.
For those who are curious, I wrote a plain English introduction to German health insurance: https://allaboutberlin.com/guides/german-health-insurance