But I suspect most students in such a case (working 19 hours a week "officially") would then resort to an additional "unofficial" job. Say private babysitting or housecleaning. With money paid without "administration involvement". :)

Always assuming of course that your official job isn´t that well paying. I mean if you need to work more than 19 hours a week, you simply have to check if it´s worth the effort. If you work 25 hours and after everything is subtracted, you only have Euro 20 more than with a 19 hour job...
In that case a 19 hour job and once or twice babysitting makes probably more sense, financially.

And of course a lot depends on where you´re studying.
I already mentioned the fixed student health insurance so that wouldn´t change. But Munich for example is more expensive than smaller university cities.