Only LA maintained state schools require teachers to have a PGCE, by the way.
Private schools and academy schools (i.e. most secondary schools in England) can legally hire and pay people as teachers without them having a teaching qualification.
The reality is that this is increasingly rare, and usually only done in academy chains as a cost-cutting measure (you can pay unqualified teachers much less). Private schools need to be able to sell a well-qualified teaching staff to parents to justify the fees in an increasingly squeezed market, so anyone with a PhD in a private school would, 99% of the time, have a PGCE too. I've worked in independent schools for over a decade and never come across a colleague without a PGCE. The 'private schools can hire anyone they like' line that gets trotted out on mumsnet all the time is a myth.
PhDs do not train you to teach, they train you to research. They also give you a very narrow subject specialism that is largely useless in the secondary school classroom, so it's not really a passport to a teaching job. It's not surprising to me that the OP's friend hasn't found a school willing to take her on, as she'd need someone to mentor her and train her.
However, as others have said, she'll very easily get onto a graduate teacher training programme, which is pretty well remunerated these days. After that first year, she will be able to pick and choose jobs, as science teachers are as rare as hen's teeth these days (unless she's Biology). It's short term pain for long term gain.
What I will say though, as someone who has been teaching for a long time, is that the PGCE is not really worth the paper it's written on. The benefit of a teacher training year is the learning on the job from experienced teachers, who guide you through the process of how to plan and teach effectively. The academic side of a PGCE is a load of bollocks - pedagogy is a pseudoscience, after all - as are MA degrees in Education and Education Management and so on - teaching is instinctive and relational, and strategies that work for one child don't for another. Teaching can't be learnt from books and writing essays - good teaching is a mixture of natural talent and experience. It can be done very well by people without a teaching qualification - having a teaching qualification doesn't mean you're any good at the job!