I worked in a secondary PRU for years, managing the emotionally vulnerable kids (those with physical or mh problems, bullying cases etc, as opposed to the behavioural referrals). We shared a site with the behavioural kids and I taught them too. I was also responsible for the Looked After Children and taught English.
Sometimes there was very little to choose between the two types of referral. In most cases (apart from the physical health ones) there was a combination of trauma and difficult family background. Interestingly, there was generally a class difference between the two sides. The mh students were usually middle class, behavioural usually working class/poor. The primary aim was always to reintegrate into mainstream or a suitable sen school.
It was the best job I ever had. Very pastoral-focused and lots of complex casework. You felt like you were making a difference to those who'd slipped through the cracks. I would agree with the OP in that socio-economic factors were the biggest influence on the students, but then that's statistically the case for all children.
In my experience its very difficult to 'blame' one cause over another when a child comes to a PRU. Of course parenting is a factor, but it doesn't happen in isolation, there are so many contributory factors - parents who themselves were abused, family history, teenage pregnancies, substance abuse, local culture, crime, mh problems, economic deprivation, employment issues, literacy problems, undiagnosed sen, even sexuality. Usually the whole family needed support, even though it was only the child who was officially your responsibility. There was a cyclical element to many of the behaviour students' families where their parents had been through the same system. When we tried to support parents who didn't have the skills to support their children, they usually had their own issues so we worked with social services and other agencies. Very hard to achieve meaningful change - there is always a root cause to behaviour issues, they don't spontaneously materialise from nowhere. I'm not saying there aren't ever one-offs such as mainstream exclusions due to violent incidents, drug dealing, crime etc but they were rare. An child who's got in with the wrong crowd or made an exclusion-worthy mistake can usually transfer to another mainstream school without too much difficulty. A PRU is not usually involved in that kind of case. I don't believe any child is just a 'bad kid' for no reason. There's always a reason.
Where there were undiagnosed sen issues, we would do our best to get to the root of the problem, and find the best future placement for that child. Again these were complex cases - very tricky to separate years of learned behaviours and history. Not that it stopped us trying! It was very rare (in fact, I don't think I ever saw it) that an sen diagnosis was an instant solution to a raft of issues - perhaps that's what the OP meant. Change was slow to achieve. Most of the behavioural students had some element of sen - low literacy, dyslexia, poor processing, global difficulties etc - and sometimes their problems had in part begun by expressing their frustrations in accessing primary education which had grown over time into a behavioural problem. By the time you get to secondary, there's a lot to unpick. We provided counselling to all students, and programmes to teach emotional regulation etc before reintegration to mainstream. Finding ways to support any sen child going forward was a challenge, as often behaviours and their own coping mechanisms were ingrained, and many mainstream schools were just not in a position to provide the levels of flexibility and support needed, especially I found with ASC students. It did make success stories all the sweeter as they were hard-fought. I think my point is that a diagnosis is far from a solution, even after it's obtained. It's a starting point.
Of course we had parents who were tearing their hair out and we were their last hope. All of my 'vulnerable' kids were under CAMHS and there was a real frustration with the limitations of the service. Also if families don't engage fully with them, they will drop the case. I worked with kids with eating disorders, depression, anxiety, bereaved and bullying victims. Also sexual assault victims on both sides of the school. These were usually bright kids whose issues combined with puberty and they felt no longer able to attend school so hid from the world at home. Sometimes we'd tutor them from home first as a stepping stone.
The parenting question is such a tough one. I'd say it's usually pretty easy to spot when parenting is a factor and when it's not. I really felt for parents of undiagnosed ASC students whose kids had been acting out for years and were often violent in the home as their frustrations boiled over. It's hard to watch. I also saw some mh students controlling their parents through their diagnosis and being incredibly manipulative - of course that's part of their raft of problems but it's a real toughie. Sometimes I desperately wished a parent would stand up to their child, but you can't say that out loud! You can gently hint, but it's a minefield as you need to keep everyone on board and it's so sensitive.
On the ADHD question, I have seen kids who benefitted hugely from medication as it's given them the breathing space to actually be themselves and start to progress. Conversely I've seen those who use it as an excuse "I can't be expected to do x as I have this condition". Even with medication there will be a need to fill the gaps in learning and socialisation which will have inevitably developed in the interim years prior to diagnosis, furthermore, medicated or not, they still need to learn self-regulation and impulse management to integrate in the future. It's a tough call and needs a multi-pronged approach.
Some kids are square pegs in round holes and a PRU can be a lifeline to finally finding a supportive, small environment where they can be heard. The stories I have heard them tell about their experiences are heartbreaking and I will never forget them. I'm so proud that I could help so many students who were struggling to find their way again and build a future. Some of my students even went on to university.
Ultimately all the students needed clear structure and boundaries, consistency, compassion and flexibility, ways to be successful and achieve, access to some aspect of education they could connect with, patience and trust. Many could not cope with change and trusted no-one. It took time to build relationships but when you succeeded, it was incredibly rewarding.