I'm well out of the loop of primary schools, but when my children were there TAs were rare, and tended to be brought in to supervise children with SEN rather than as more general assistants, although there was one qualified teacher who didn't want classroom responsibility but ran all sorts of things (lost property, book sales, the organisation of music lessons - that sort of thing).
Otherwise it was down to volunteer mothers, many of whom had too much time on their hands, and they caused no end of problems. They would see a snapshot of a 'situation' in a classroom, and gossip at the gates about the teacher's ability to handle it, the child's behaviour, the child's ability, what they would have done better, and so on, all without any context, training or understanding. Some would go in every week, and treated it (in their heads) as a job, so became an unelected, unqualified and uninterviewed 'key person' to organise parents and take on roles they hadn't been asked to fill. Obviously the gossip would get back to the mothers, and there were 'she said that she said' situations on a regular basis, that must have been exhausting for the teaching staff to handle diplomatically.
I think it is far better to have TAs who are staff, so subject to rules of confidentiality and so on, and who are limited in scope to what the teachers actually want them to do. It is also only fair that the role is a paid one, as it is clearly important. Also, Heads can tailor the training of TAs to the needs of the school, eg a friend of my daughter has a boy with pronounced ADHD, and the TA has had training in dealing with this so she can be of more help. I think the idea is that she will follow him up the school, but obviously her training can be applied to other children as needed too.
