Yes, I definitely think parents have significant power to change.
I do think part of the problem is that this relates to the teaching retention crisis. When I did my teacher training and nqt, a million years ago, the safeguarding training was very brief. It was inadequate.
Thankfully, I had an experienced mentor who led me through how to deal with my first safeguarding issues. One of which was year six children had found their parents YouTube and used it to browse porn. At the time, whilst I thought it was awful, I didn't realise it was child abuse and we had the power to further escalate it. Thankfully, having an experienced teacher to guide me I was able to follow the proper channels and retained that knowledge got the future.
But we have a lack of experienced teachers and mentors now due to the conditions in teaching being nigh on impossible. So new teachers don't get the wealth of knowledge and experience and rely on their own preconceptions, which as demonstrated elsewhere on this thread, can be naive, wrong or actively a safeguarding issue in themselves.
I'm not being ageist, btw, the mentor that actually taught me was young in herself. The point being that experience is not valued in education and no effort is being made to retain those staff.
And furthermore, often what you will find is that SLT are relatively inexperienced 'climbers' whose experience and knowledge is limited. I've been in teaching a long time, but I am not a climber, I stayed in a lowly position because I don't want to be a paper pusher out of the classroom etc, but the amount of times I've been overruled by someone I've known demonstrated more is numerous.
And sometimes, that has adverse effects for the children. A few times it's been really serious.
But each time the SLT finds someone lower down to pin blame on and the culture never shifts.
I'm sure it's not like this in all schools, my husband has a very different experience, although we both acknowledge his concerns get listened to more by virtue of his sex.
Anyway, rambling somewhat, but my point being this is another symptom of the crisis in teaching and it's awful that nothing will be done until children are collateral damage.