WRT how unis use the PS:
My understanding is that a lot of unis use the PS as a sort of basic filter- if it's really badly written (not as in a few typos, but really poor grammar, very difficult to follow, or the applicant writes something truly bizarre or shocking or offensive) then it can be used to filter applicants out at an early stage.
Some for some courses will also filter out applicants who are clearly applying for a wide range of courses or very different courses and this is usually obvious from the PS.
Some unis will then use the PS to decide between similar "borderline" applicants when deciding who to offer to.
Some unis use the PS as part of their selection process as standard, and they'll usually have additional advice on their website about what they want to see.
Some unis will use the PS on results day, to decide between applicants who have missed their offers if they have say 10 places left and 20 people who got the same grades.
Some unis will use the PS if applicants apply via clearing, as well.
I don't think there are many (any?) unis that openly state they never read the PS, because they may want to use it in certain circumstances. But some definitely put more weight on it than others. Those that value it a lot will usually mention it in their admissions requirements or on their websites somewhere. Courses that interview obviously put less weight on it.
OP- To get your daughter started, could she just write a paragraph on why she wants to study history? Tell her not to worry about extra curriculars or reading or anything else for now- just get the basics of why she wants to study history on paper. I find with perfectionists, once they've written something, it's easier to keep going!
But if she's finding that genuinely difficult, are you sure history is the right choice? I'm not saying it in terms of academic capability- but if she can't articulate why she wants to study the subject, then is she sure it's the right choice for her? Sometimes people struggle to write the PS because actually, subconsciously, they'd rather be applying for something else!