Why would she be stuck I housekeeping forever? The point of early career is that you gain experience in the workplace, and that you move into something you want to do longer term.
I had a string of low paid, physical jobs from age 15 while studying for exams and then while deciding what I actually wanted to do. I worked full time while studying for a professional qualification, made possible by not having children and responsibilities so my energy could go into earning money and improving my employment opportunities.
How will she get a foot in the door if, at 20, she doesn’t work because she doesn’t need to? The perfect job isn’t just going to appear for her, and if it does is she really going to be employment ready and have the skills and knowledge to make a reasonable application? Early career jobs have always been hard work for not great pay, but that’s where you start not where you stay. It takes effort to build a life, to stand on your own two feet as an adult. It means doing jobs that aren’t your preference, developing a work ethic, and learning workplace rules and routines, and working towards what you do want to do.
If she were my child I’d be encouraging her to give it her best shot, helping her cope with her work pattern and helping her decide what she does want to do in the longer term. It’s a shame it took the job centre to insist she takes a job, I’d have been giving her that clear message long before she reached 20.