If a LA can't even cope with its failing schools, what makes you think it's got time to interfere with it's good and outstanding schools
The simple fact that they do. Schools in those authorities don't get tonnes of autonomy regardless of how they are performing. And any LA controlled school has significant limits to its autonomy.
The evidence from around the world, in any event, shows what the person using it wants it to show
The evidence seems pretty solid. But, as AmberTheCat says, it also shows a need for sound accountability. The two are not in conflict. Ofsted inspections make the school accountable. One can argue about how well they achieve that but they certainly don't take away autonomy. They can't tell the school what to do.
Your interpretation of autonomy seems to be that schools are free to do exactly as they like in all areas with no accountability. That isn't what it means.
And why were LAs as a concept the problem in all this, rather than it being a case of some LAs not doing their job properly? It seems to me that the big problem in this country was not LA interference, but interference from central government.
You are entitled to your views but they are in conflict with the evidence. Around the world it has been found that giving LAs (or their equivalents) control of schools produces poorer results.