If you are self-employed, the public insurance is really nothing more but another (rather unattractive) insurance company you can choose from.
I agree it doesn't make sense from a financial perspective generally but it does depending on your health records/situation. I, for example, have a chronic disease which implicates monthly medication which is crazy expensive. I could enter a private insurance (because I have a Anwartschaft, thank god I kept this from since forever) but the monthly rate will drive to insane amounts when I'm getting older and/or adding the fact of kids (Familienversicherung).
Going back to public insurance after being in private insurance is highly problematic and probably even impossible without playing grey-zone games if you don't want to lower your salary dramatically below the income border for multiple years.
Disclaimer: my knowledge is based on internet research, I am not an expert on this and might be wrong.
AFAIK if you are self-employed the gov insurance doesn't have to take you either! Yet both have to take you using that "base tariff" (600? Euro or sth) since a few years (before a self-employed could end up w/ no insurance at all, not possible anymore).
It is true that the private insurance increases significantly over the years, but it is still WAY less than the gov insurance. The costs for the gov insurance is about 25% of your salary (remember, it's split between employer and employee, but as a self-employed you have to pay both sides). Assuming an income of just 5k per month, that would be 1.25k! per month, or more than twice the base tariff.
It often becomes problematic for self-employed low-wage workers when they enter pension. Which they often don't setup, and hence can't even pay their health insurance :-/ (and then move into social security, which again provides everything)
That it is difficult to get back to the public insurance is just non-sense unless you exceed a certain age. In fact you have to, whether you want or not, by law.
It's actually about 15% in total. The maximum amount currently is around €750 for both employer and employee.