Interesting question about whether the 'better' PTAs are associated with Good and Outstanding schools.
First of all it depends what you mean by better PTAs. If you mean those that are run by carrer women and ex career women, who have the ability to organise on a professional level and rope similar people in to getti g involved,attending and spending big bucks at their fundraisers, then probably yes. Although by no means in all cases (before people jump on me) a lot of Good and Outstanding schools are in affluent areas, with this kind of parent. See the post earlier from someone with children in private school who talked about the highly professional events organised by the PTA which was made up of ex high flyers, which could raise thousands and ours ands for the school or charity.
It may well be too, that in affluent areas, there is a stronger sense of wanting to be involved in education (again, I'm not saying this is exclusively so) and so in these kind of areas there is more parental involvement as classroom helpers, as Governors, as PTA members etc etc.
However, I would imagine that PTAs can be excellent in many Requires Improvement and Special Measures schools too. Sometimes the parent profile is exactly the same. And where it isn't, parents can still be keen to be involved. I suspect the sense of COMMUNITY is very important in determining whether PTAs are good or not. There can be a strong sense of community in less affluent areas too. If there are less people from high flying backgrounds, they may put on less polished events, but they maybe better and more fun as a result of that. Equally in some areas of real deprivation, it maybe hard to recruit people for a PTA because there is simply no one who believes they have the leadership skills to run one.
Clearly there are lots of generalisations here. In all types of school there a people who are busy, busy working and can't get involved. There are also those who don't want to be involved for the variety of reasons on this thread. I guess the thing that would be interesting is to see what %of parents in the different school types attend a PTA event during the year. We know that fewer parents attend parents evenings in schools in deprived areas, but is that also true for things like PTA events.
In my experience of 2 schools, one which was Satisfactory and in a reasonable area and the other Outstanding in an affluent area, the schools truffled for parental support in the Satisfactory school, it wasnt just the PTA, but when the school put on a Maths evening or had an Info about SATS evening etc etc very few would attend. The events were evenings not days. When the other school put on similar events, everyone pretty much would be there. People who find babysitters, make sure their late working husbands were home and get to the event. Attendance was similar for PTA events too, although in both types of school, there were plenty of people who did not help run the events.