I got some letters about that and they asked me to prove that I was indeed self-employed. They didn't like the argument and concluded that I wasn't. The only thing that actually happened after a while is that I had to pay into the public retirement fund against my will. The "Deutsche Rentenversicherung" are seemingly the only people that care. From what I can tell there were no other obligations/rights that appeared after.
There are different parts of German law/government that are affected, retirement is only one of them (and just because one authority noticed/thinks you qualify doesn't automatically mean that the others do).
Tax avoidance (since payroll taxes on your salary weren't paid) is another angle.
For the employer, not paying their part in your social security contributions is similar to not paying you your full salary, and thus a criminal matter as well.
Ordinary self-employed people and sole traders pay nearly the same tax rates as employed people (National Insurance, a strange disguised tax, is at a different rate), but have many fewer rights, eg. no right to paid time off or sick pay.
The question in this case is whether Uber drivers are self-employed or not. Not as it turns out.
What on earth are you talking about... taking out dividends is not illegal, even for individual company owners. IR35 is about HMRC forcing self employed people to apply payroll taxes as if they were employed. Again, nothing to do with dividends.
Very similar here in Germany, I guess. There is the term "Scheinselbstständig", which roughly translates to "fake self-employed". If you are formally self-employed but meet certain criteria, your "customer" (who is then considered to be more your employer than a customer) has certain obligations to you, and you have certain rights, which you can't easily trade away.